This is something I've thought about a lot. And I've come to the conclusion that there's only 2 games I know of that I would consider art.
The first, is Okami.
This is my favorite game. For many reasons.
First of all, it just looks amazing. All the characters and areas are well designed, and in a very appealing style, no less. It tries to use its own, traditionally-inspired style, which works very well for it. Likewise, all the characters are written well, have their own personalities, and aside from a few one-off characters, are very memorable (Especially Waka ). The gameplay varies between consoles, but the Wii version absolutely nails it for me; while it can be wonky at times, this game does its best at showing just how great motion controls can be. It plays out like a standard RPG with real-time fights, meaning that reacting to enemy actions is often just as important as your own attacks. An area where this stands out the most is the boss battles. OH JEEZ, THE BOSSES. They each have their own quirk to them; just attacking won't get you very far. They make you use your abilities quite a bit, and in creative ways. Speaking of which, every ability you get remains relevant throughout the game; not one becomes obsolete. Have I mentioned the music yet? If not, go check out the soundtrack of this game; there's very few tracks that aren't amazing. There's also TOOOONS of side-things to do that'll keep a completionist busy for days.
I think I've text-walled this one enough. Suffice it to say that this game is amazing in nearly every aspect. It does have repeated bits later on, but it's mostly boss battles, and as I've said, the boss battles in this game are universally good.
Second, we've got Dust: An Elysian Tail.
Y'know what I said about Okami? Pretty much copy and paste it here. But, in some areas it's better, and in some, it's not. The main area where this game is better is in the characters. There are less of them, yeah, but the ones that are there all have their own unique charm. Whether it be the calm and collected Ahrah or the insane antics of Reed, there's enough uniqueness here that everyone is memorable. That said, the game is pretty short if you don't do everything. Which is fine, since it does what it needs to; I'd likely have liked it better if it were longer, but it's still great nonetheless.
But, in my eyes, the make-or-break part of any game is its storyline. Which is something these games don't just do well. These games tell two of the greatest stories I've ever heard. They have their happy moments, they have their sad moments, and they have their angering moments. Most games I've played can achieve these on some level, but these two... They go above and beyond the call here. I have never felt stronger when playing a game than I did when playing these two.
When considering looks, characters, gameplay, music, content, and storyline, these games are both beyond amazing. Art is a term I use strictly, but these two? They've earned it.