Oblivion. Though it's up to debate whether it's a RPG. But because enemies scale with the player, basically it's like you don't get stronger (relatively to the monsters).

Or maybe Ghost of a Tale....

Then that would make every PC game where you play as another character an RPG.

Doom is an RPG cos you're role playing a space marine
Command and Conquer is an RPG cos you're role playing a commander
Call of Duty is an RPG cos you're role playing a soldier
Sam and Max is an RPG cos you're role playing detectives

See the problem yet?

There are skills to level up and each 25 percent to that skill gives you a perk. As flawed as oblivion was, there is still a system of progression

Yeah .... that's indeed a very strange question, especially coming from you, since I always had the impression you have a much stricter definition of what an RPG is than most other people. But even I who's usually much more lenient with the genre definition would say that it's very debatable whether a game without growth system can even be called an RPG. Unless you explicitly state your definition of an RPG, excluding games "whose RPG-ness is debatable" sounds like a pretty nonsensical request to me, especially in this context. One could almost think you were trolling ...

I consider System Shock 1 a kind of RPG survival, even if there aren't character stats or levels.
The only improvements present are limited to the items you'll find.

He was being a smartass/troll. We all know what RPG literally means - we're talking about a genre of computer games.

Oops. the smartassery/trollery obviously went over my head there *facepalm*

Getting bigger. Not just physically, but also mentally and spiritually, sometimes even sexually (The Witcher games).

I would say the game "Squad" belongs to that category. Many others too like Quake and Doom.

https://www.giantbomb.com/rpg-7/3055-682/games/

I presume this was the answer you were looking for?

Some of LARP games, expecially historical reenactment variety.

Kind of iffy about that since I know the MMOs I play, the enemies get harder as you level and move thru the story lines.

Well there are MMORPG's without progression and that has RPG in the name.

Minecraft, Roblox, Club Penguin (RIP)

I thought you could gain some kind of levels in Minecraft? Anyway, can't really say I ever thought of Minecraft as an RPG, but with all the genre mixing that goes on these days, who can tell what's what anymore.

I want one with a battle system that is recognizably an RPG battle system; I'm thinking something like Wizardry or Dragon Quest here. The way I see it, an RPG has an RPG-ish battle system.

A pure adventure game does not have a battle system at all; any combat in such a game is scripted and treated as a (adventure-style) puzzle. This game (and its Game Boy predecessor) are really action games that happen to borrow a few elements from the RPG genre. Of note is that the dungeons consist entirely of action stages with no "out of combat" exploration found at all. Also, you gain jump height, wing strength, health, and even a few different shot types as the game progresses (though it's progress-based rather than level or exploration based). Actually, in Morrowind:
For Any%, a glitch is used to boost certain stats (Speed and Luck included) to absurdly high levels.
For All Main Quests, the glitch is still used, but in addition, the player actually does level up to level 3 (as it's required for the main quest) by raising the Mercantile skill.

Also, even if the player doesn't use it, the growth system is still present, and the developers still designed the game with the assumption that the growth system would be used.