Strategy. Specifically I play chess, civ 5, and DOTA 2 whenever I want something quick, fun, and engaging. I can go up against a grandmaster level opponent while I wait for something to update or load.

But I play anything and everything that's not subscription based, overpriced (call of duty/overwatch/etc.), or visual novel/hidden object/crappy art indies/crappy 3d indies/politically correct. I don't mind basic looking games but when it's grade school art or the animations are lacking I can't get into it, or things with drama around them like Mighty No. 9.

I also have a soft spot for fighting games and platformers.

Shmups. I really enjoy the accompanying adrenaline rush.

Turn-based RPGs. Especially fantasy/magical ones.

Fantasy 4X games are fun too.

Well made platformers with RPG elements or a 3D action-adventure that usually has a combination of interesting gadgets and a theme that makes it feel you aren't just a soldier killing stuff for no reason.

Occasionally a slower strategy game.

Usually a racing game which is my most played genre anyway, or a simple arcade game like pinball or a shmup.

A lot of them. Strategy, RPG and P&C for sure. And I really like fast-paced platformer games that can be played just for a fifteen minutes or so and still enjoyed. Spelunky and Rogue Legacy are the most prominent examples.

To me, my notion of RPG happens to exclude games like Zelda 2 (and the entire Zelda series, actually) and Secret of Mana, which I happen to consider to be action games. That, of course, doesn't mean they're not fun (I believe I mentioned Zelda 2 being a good game where it feels I can get a lot done in a short amount of time); I just don't consider them to be options when I am looking to play an RPG. (Maybe I need to replay Zelda 2?)

The problem with the games you are thinking of, from my perspective on this topic, is the following:
1. When the quest is small, it doesn't feel like much has been accomplished. It's only when I can complete multiple major quests, those that contribute directly toward the completion of the game, in the space of a half hour or so, that I feel like I have accomplished a lot in a short time.
2. When a gaming session is spent primarily with story sequences, it feels like nothing has been accomplished; when I am looking for a game to play, having to watch story sequences just doesn't feel fulfilling to me.
3. Sometimes, I want to have fun *without* progressing the game or consuming side quests. That's why I sometimes like to have options for what you are calling "grinding" (I prefer the older term "leveling up" for this sort of thing). (Remember, side quests are usually in finite supply.)

Side note: as an addendum to 3, I prefer games where town NPCs you kill respawn when you leave to those that keep track of which NPCs you've killed longterm.

Leveling up or learning more about the story or gameworld in small doses are forms of progression to me, too. I guess we just have totally different preferences and perspectives.

RTS (real-time strategy) is one genre where I generally feel relaxed. I know there won't be anything to write down or trying to memorize (like what quests I was supposed to do next in RPGs, even if having a several week hiatus from the game). I can pick up a RTS save game and continue from there without any problems.

The learning curve is usually quite low (RTS games usually introduce you to the gameplay bit by bit, by starting with simple and easy missions where you start from the basics like merely harvesting resources). Nothing like Icewind Dale 2 where I am supposed to first read a manual to even understand how to create a party and characters that don't totally suck, or some Master of Orion/Master of Magic/Civilization where I am completely lost in the beginning if I don't memorize the whole manual.

Also, I hardly ever get seriously stuck in RTS games, usually I do some progress each time I play it. So it is not like some point&click adventure game where I might be stuck forever in one tiny puzzle or item hunt, unless I read a walkthrough.

So, yeah, I guess for me RTS games have the least annoyances that might make be bored or frustrated by the game.

When I'm bored and I don't want to read through walls of text or I don't have much free time for longer sessions or don't have the energy for tactical/strategic planning, I go for FPS, racing or RTS games -- I completely avoid Grand Strategy/TBS, Adventure & cRPGs.. When I'm bored but have enough time, I usually start an aRPG for mindless hacking & slashing.

For leveling up, I have found myself, in many games, worrying about accidentally over-leveling; perhaps it's because too many JRPGs are not particularly well balanced in this respect, or the balance is a bit too precarious (in the sense that 1 level makes too much of a difference). It is for this reason that I sometimes prefer games that expect you to level up as opposed to those that don't.

Learning more about the story/gameworld is something I sometimes enjoy doing, but there are a couple catches:
1. I need to be invested in the actual gameplay first; if the game bombards me with story before I even get to control my character, I find myself uninterested in the story and get impatient wanting to actually *play* the game.
2. Once I am invested in the gameplay, my preferred way of learning about the story/gameworld is by talking to random townspeople (in towns that are preferably of manageable size and don't have random triggers strewn around). The nice thing is that this can be done without having to progress through the game or consume side quests. (It helps if there is a spell that lets you warp to any town you've visited; one thing I like about the Dragon Quest series is that, starting from the 3rd game, such a spell exists.)

Adventure games are an easy go-to game when I don't know what to pick up next. They're easy to get into (unlike RPGs, which have a learning curve), and there are plenty of good titles, both new and old.

RPGs.
Roguelikes, sandbox, open-world type for when I'm looking for something to kill time with.

Have you checked out Osiris New Dawn yet?