For those with any doubts, the question is definitively answered by a game I just finished: Shadow of the Colossus.
It's an amazing work of art. Period. Visually, it has a distinct style that's almost impressionistic. Musically, it makes you feel tension and excitement and sadness, like any great film score or, hell, orchestral composition. Game play wise (a unique aspect of art for video games), it boils everything down to its simplest possible elements. This is a complex game that doesn't even require all the buttons on the PS2 controller. And the game manages to be challening without almost ever becoming frustrating.
In a really great innovation, the game is challenging and takes a while, but you rarely die. Instead, you can spend 30 or 60 or even 90 minutes alive battling a colossus. After all, what's the point of dying and starting over? For this game, at least, that would be a really artificial interruption, it feels like.
Narratively, it's unique and extraordinary. There is only sort of a story. It's there, I suppose, but it's only relevant at the beginning and end. The main character, who you play as, doesn't even have a name. It's too abstract a game for things like that to matter.
Most importantly, the setting and visuals and a pace create real feelings. When you're riding through an empty land to find a colossus to battle, you can feel the loneliness and desolation. And when you defeat a colossus, you feel sadness.
Why? Because this is, amazingly, a morally ambiguous game. You're defeating 16 colossi (I didn't know that was a word either) to bring someone back to life, but the colossi aren't attacking anyone. They're living peacefully in this isolated land. You're hunting them down and murdering them and the visuals and music make clear this isn't something to be celebrated. Each victory for the player is a little sadder.
By the end of this game, I felt genuine sadness. People ask if a game will ever make someone cry. Well, I didn't actually shed tears as I did at Brokeback Mountain, but I felt genuine sadness at certain events I won't give away near the end. And in the final scenes, things switch up in a really fascinating and exciting and artistically interesting way. At the very end, the gives control back to you from what was a cutscene at a crucial moment. I won't say what happens, but it lets the player personally experience a feeling of desperation that's throughout the finale, but is so much more palpable because you yourself are, fruitlessly, fighting it.
Video games are art. And this is, in my humble opinon, the greatest artistic achievement the medium has known. (Though Katamari Damacy is a close second, albeit for very different reasons).
BTW, no surprise that Shadow of the Colossus swept the Game Developers Conference awards. And no surprise it lost most of the gamer magazine awards to Resident Evil 4. This isn't the kind of game that the core 16 year old gamer would appreciate.