Skyrim

Not according to the way I define "RPG".

Would you say that action games should not include any action, shooter games should not include any shooting, racing games should not include any racing, because it's all superficial "icing", perhaps?

VN are interactive books, they don't allow or have all that much to do with said role-playing and freedom to customize and act out the character you want. At least, not since the text adventure games faded into undeserved obscurity.

Role-playing games at their very essential core are based upon the premise of fitting into the skin of some character, acting as them, growing as them, making choices, and optionally (as there are RPGs without many choices so there also are RPGs without any meaningful customisation), customising their appearance, skill set and equipment.

So yes, you are attracted to what was originally the icing - and long since became its own genre. That genre is nether here nor there, I just don't much approve of reducing all sophistication of role-playing in role-playing games to green [AGREE] and red [DISAGREE] and similarly uninspired conversations framing the choice, if even that.
Charisma is useful for NPC's reactions, ability to persuade them, efficiency of inspiration, buffs/debuffs and other face/leader/bard work, and any role-playing elements at all, but if you don't want to have them period you can do without.

Still, if you want to reduce attributes to bare minimum there's absolutely no reason not to fold Strength and Vitality together; each of three attributes can contribute to defence in their own way, be it shrugging damage, dodging or parrying, arcane or technological means (heck, you might make enemies less likely to attack a character with high Charisma, and maybe switch to their side, even), but it's a given that the burliest character would generally be the toughest.

And if some core stat in minimalistic setup is useless, say, if hit chance and bonus damage of all attacks is determined by Dexterity, and Strength only adds to unarmed damage, of if Charisma doesn't do anything useful at all, well, that's entirely the fault of the game designer, not the attribute itself. Just like it's the fault of the game designer when attribute list contains two or even three iterations of the same quality, like, say, Agility and Dexterity, or Constitution, Vitality, Endurance and Stamina at the same time.
Well, what Diabloids lack in affecting the story department they make up in character building and combat, although I do believe that any game can be made greater by including both aspects.

To me, the resolution of actions via stats and die rolls is the core aspect of an RPG, in the same way that real-time combat with collision based resolution is the core aspect of an action game.

Acting as a character can be done in other genres, like in action games. Having action success be determined by the character's skill, as opposed to the character's skill, is something that doesn't happen in other genres. (See games like Oblivion and Skyrim for examples of what you refer to as "role-playing" in games I don't consider to be RPGs.)

I would of course agree that resolution of actions via stats and die rolls is one of most common features of role-playing games, but it's facilitation, not the core. Means to an end from the times before computer was a viable medium for games, and even then, ubiquitous. but hardly essential. The core is role-playing, hence the name.
I don't know if you forgot that tactical, strategic, economical and games of other genres that feature distinctly statted characters and use those character's stats, random rolls and other character's stats if needs be to determine the outcome of any action those characters undertake exist, or are you merely uninterested in them, but this is something that indeed does happen in other genres.
So I gather your definition of RPGs is entirely at odds with any encyclopedic or commonly accepted one, then. I mean, you might not like TES, but you can hardly deny that it's one of most well known RPG series, and they're certainly much closer to tenets of the genre than any would-be procedurally generated grindfest, good as the latter might be in its own right.

I never stated anything about not liking TES; all I stated is that Skyrim isn't an RPG.

I can't deny that the series is one of the more well known series, but the games, particularly Oblivion and Skyrim, don't actually qualify as RPGs due to the core gameplay being that of an action game.

Also, the first two Elder Scrolls games, Arena and Daggerfall, are mostly procedurally generated (albeit done only once by Bethesda or with fixed seeds, particularly in Daggerfall). Also, don't forget what Skyrim calls "radiant quests", which appear in Arena and Daggerfall and *are* procedurally generated.

What about the type of RPG where the final boss is actually a guy that can be shot in the head and the game ends? And there isn't like some high level enemies or boss character to beat before him, that's it. You've resolved the conspiracy.

This is also a dumb take. The problem with Skyrim being an RPG is that it's bad at having any meaningful consequences and utilizing its resources in order to facilitate roleplaying better, not because it doesn't use RNG to resolve conflicts. It being an action game doesn't disqualify it from also being a roleplaying game, which it is even if in a half-hearted way.

Or the type of RPG where the final boss is a townsperson in the first town, and if you kill him early (perhaps with the help of other people in the town), it gives you the ending? (Two Worlds before a certain patch)

Or the type of RPG where you're asked a question during the intro (before you gain control of your character), and a certain choice gives you an ending? (Metal Saga)

Or the type of RPG where you can go straight to the final boss at the start, but probably won't win? (SaGa Frontier, Lute's scenario)

Actually, it does, the same way a game like Nethack or Civilization being turn based disqualifies it from being an action game.

But if you think about it, having character stats determine success is role-playing, because it means you have to play in a manner in which that character, with their attributes and abilities, not you with yours, would succeed. Past that, there are degrees. You can say that, from this point of view, a game where the character matters 100% and player skill has no relevance is pure RPG while one where character has no relevance and player skill is 100% is pure action, but there's a lot of room in between, whether it's one of the genres with minor or modest or notable elements of the other or a "full" action-RPG where the two mix in similar amounts.

It is as RPG as a game gets. TES games might not be liked by all, but they objectively are role-playing games with all essential features and broadest selection of optional bells and whistles such games might have, and as opposed to games that are lumped in with RPGs despite not having any role-playing nor even giving the player any leeway in protagonist characterisation. I mean, including those because they share a mechanic common to RPG subgenre hurts nobody, but how do you go from that to defining the entire genre by narrow example of such mechanic, all while excluding the real genre-defining feature and game from it?

There's no strict requirement for an RPG to be turn-based, isometric and use character stats and dice rolls exclusively to determine everything rather than augment player's own skill by traits or abilities they chose or developed, it's irrelevant what sort of combat or perspective a game runs. If it's got role-playing or player-guided protagonist's development in its core it's an RPG.
Naturally. If you want to create a large, lively world, handcrafting everything isn't really efficient way to go about it, and some randomness spices things up. But that isn't the point, which is: the game with role-playing as its core is a role-playing game more than a game that shares some mechanical aspects with some RPG subgenres but lacks role-playing itself.

It's just another case of your definition being at extreme odds with both textbook one and somewhat narrower ideal I believe the games of the genre should aspire to, so I reckon it's another sort of an issue we can endlessly go back and forth.
Points for realism, although there's a lot of other factors that would determine if the game is good or bad.

It isn't, no more than pencil's graphite is a poem made; I already mentioned that it's used by games of many other genres that make use of unique, or at least sufficiently randomized characters; it's just an approach facilitating gameplay, and it's as valid as any other. Sometimes less, if there's no real role-playing to speak of - no opportunities to take different approaches to objectives, problems, and social interactions, no said social interactions to speak of, no ability to shape the story and leave an impact by making myriad choices here and there, no ability to guide and shape the player's character growth and development...
That's what makes one game more role-playing than another, it doesn't particularly matter if your success at said game is decided by clicking the enemies to death, clever manoeuvring, ability use and conversation choices on your part or hard-settled by your character stats, or if all those stats are utterly superficial.

A lot of arguments seem to revolve around satisfying certain tropes that fit whatever ill-marketed conception of what a roleplaying game is meant to be. I'll agree that an RPG is more of a sliding scale, but I prefer to think of it as a world to interact with and immerse oneself in as opposed to being a series of "press buttons to level up and watch a cutscene".

I'm of a similar mind on this; the latter and whatever mechanics specific to a given RPG flavour might well be there, but it's the former that really matters.

And there are also games that depend on player skill but have nothing to do with action. Like strategy games that require tactical thinking or puzzles that require math/logic/encyclopedic knowledge.

Both had their perks. I used environmental occlusion and movement quirks to my advantage more times than I recall, though obviously that was in multiplayer. But nowadays, I reckon, there's no reason not to make use of player-customisable camera. Other than nostalgia and tight budget, that is.
The problem is that your definition focuses on an irrelevant, when it comes to defining the greater genre, gameplay feature that isn't even an attribute unique to RPG, while disqualifying a solid majority of true, proper role-playing games. There's nothing clear or sensible about it, it's even sillier than, in a similar vein, claiming that strategies can only be turn-based and real-time strategies aren't strategies but actions.

And there's nothing "way too broad" about immersive role-playing in interactive world that usually features character development and customisation which is the basic, strict definition of the genre, "too broad" only begins only when you start adding games that lack all of that but purely mechanical stats and stat-based rolls - that are, again, a staple of tactics and many other genres, and not something unique to RPGs. And even then I would say it's better to include roleplay-less turn-based number-grinding outliers than throw them out or try to stretch them over RPG genre proper and throw out everything that doesn't share their narrow approach to gameplay.
Again... You cling to thoroughly unsuitable definition and exclude a fundamental chunk of the genre for no good reason. There's no "RPGs and other turn-based games", RPGs may be turn based or real-time, top-down or first person, use keyboard and mouse, or mouse alone or even a gamepad, stats might decide everything, might help the player leverage their own wits and control input better, might barely even matter. Just call things their own names, call role-playing games role-playing, call turn-based games turn-based, clarify if the game doesn't neatly fit somewhere, you aren't really helping crippled and otherwise disadvantaged people by claiming that wast majority of the RPG genre doesn't count, and you can damn well suggest some good turn-based games that can be played with one hand and whatnot to them without that.