What game do you play (or want to play) mainly for the art style?

I'd love to play Cuphead purely because I love how it looks. But unless it's ever a giveaway I never will, because by all indications I'd dislike the actual gameplay quite a bit.

Yes! That game makes me wish there was a Popeye game in the style of the early Max Fleischer Popeye cartoons.

I would have to think that -- for me -- Darkest Dungeon is a game that I played solely (at first) for the art style.

I would put Banner Saga here but... although I've started the tutorial multiple times, I can't say I've actually played it.

I'm not sure I would play a game mainly for its style... but looks can certainly play a big part in sparking interest for a particular title.
Among the games I've played, Machinarium springs to mind. I don't usually play point-and-click adventures, but this looked too interesting to pass up (I like Amanita's style!).
There are a couple of games I'm going to play in the very near future, that actually attracted me by their visuals, namely SYNTHETIK: Legion Rising and, even more so, Spinch.

I also very much like retro-aesthetics, when done well, so I can mention:
Blazing Chrome
Huntdown
Super Catboy
Cyber Shadow
Cyber Mission
Super Cyborg
Axiom Verge
Oniken
Volgarr the Viking
Odallus: The Dark Call
Valfaris
Vengeful Guardian: Moonrider
Gunborg: Dark Matters
Gato Roboto
Bzzzt
Tower 57
Xeno Crisis
Prison City
Shadow Gangs
Steel Assault

Really, there are a ton of those... and all those "boomer shooters" as well, such as HROT, Ion Fury, Boltgun, Project Warlock, Prodeus, Perilous Warp etc. you know the stuff.

Other games relevant to the topic at hand:
XIII
Headlander
The Deadly Tower of Monsters
The Swapper
Blasphemous
CLARC
Creaks
Iron Marines
Silt
Shadow Watch
Wrack
Tokyo 42
The Plane Effect
TOEM Yeah, Cuphead too, although it's (still?) a bit expensive for me.
Perhaps you're aware of MOUSE? Scheduled for release on Steam in 2025.
The devs have stated they're potentially open to publishing on GOG, even though nothing's set in stone at this point.

wishlist: https://www.gog.com/wishlist/games/mouse

I'll stick to games I've played or else the list will get too long.

The Banner Saga trilogy
Forgotton Anne
Gibbous
Irony Curtain
Out of Line
Paradigm
The Plane Effect
Shardlight
Unforeseen Incidents

Usually I don't play a game just for its art style, however I have to admit that I'm intrigued by Return of the Obra Dinn.
Cuphead and Darkest Dungeon look quite unique too.

I consider the art style, direction and design of secondary importance, behind gameplay and control scheme but one game that had grabbed my attention was SuperHot. With very simple graphics, the dual tone palette is very well done. Reminds Mirrors Edge but much more extreme.

Cuphead and Darkest Dungeon not only look good but are very good games. Return of the Obra Dinn does indeed look very interesting but didn't play it.
One game that the art style grow up on me over the time is Battle Brothers. Instead of going maintream with pixelized art, simple animations backed up with great sound design makes the no arms and legs design quite enjoyable, board game alike.
Nowadays every freaking game seem to be over saturated, over vibrant and over colorfull (I call them mobile-like) but Bastion does looks very nice, specially considering it's a old game (just checked: 2011).

Mortal Kombat is a game I start playing mainly for the art and gore, back in the day.

Honorable mention goes to Minecraft, not because is enjoyable but had set a freaking big trend (too big pehaps).

Any hentai-game

Jokes aside, I do love the artstyle of eg. Sword & Sworcery, Gris and Okami

What did you think of Below?

Huh, I didn't know that one. Thank you for hint!

The graphic design looks really good. A bit gloomy though, but it fits the setting.