Tetris

Ultrakill. Sometimes guys will talk to you, but its rare (only before bossfights), can mostly be ignored, and can be skipped after listening to it the first time.

Dead Cells, you can even turn off 'lore' in settings.

Return to Castle Wolfenstein? The new Wolfensteins have quite a bit of story, but the old one is all skippable.

I’d have to recommend Untitled Goose Game, Goat Simulator, the Karamari series, and music based (do the thing to the beat) games like Dance Dance Revolution, Taiko Drum Master, Guitar Hero, etc.

Sky Rogue. This is a great arcade game, very replayable.

w40k Gladius?

I hear ya, I hate when games have too much story. The stories are never any good and usually outright eye-rollingly bad. I particularly hate when they do "..."

Legend of Zelda, the very first one. Yoshi's Island. FIFA.

Disc room is such a fun game and it has almost no story

I finally got superhot: mind control delete during the summersale. Very simple but engaging combat mechanic, and story is kept to a minimum

I know Axiom Verge has a Speedrun mode that cuts out all the cutscenes, I don't know if that qualifies though, and you do kind of have to know what's going on outside of that. The story itself isn't necessary to enjoy the game though.

Victor Vran's not much for story but the game is fun. You can even find a weapon that launches exploding chickens.