Ah, a topic I have strong opinion on (IE: All my opinions.
)! Anyways I think Deadeye is right, through and through. Which saves me a lot of posting, but I will still elaborate.
First, I think the definition of art is something that needs to be understood a bit. Okay. To a degree, everything is art. A teacup made by a silversmith, even if plain is still a form of art. It is art as a craft. Basically every human creation can fall under this to some degree or another. But that definition is not important. We need to be talking about SIGNIFICANT art. If your definition includes "All games are art!" Its not really a useful distinction from a discussion point of view. The same applies for all media. Epic Movie and Citizen Kane should never be in the same category of 'art'. From here on out when I say 'art', I mean significant art.
What type of media has the highest percentage of 'art' in professional works? Paintings, clearly. Why is this? Paintings are a limited media. You can not tell a narrative in a painting (unless you use several!). It's hard to be 'funny'' in any significant and long lasting way in a painting(but it of course, is -- and hard enough to then roll back to being art). You have to be very symbolic, expressional and technical to portray a feeling, emotion or lesson with any sort of accuracy.
Movies on the other hand , while definitely possessing artistic entries, has a wiiiiide variety of indulgent movies. Comedies, slashers, big explosions. They don't need to be art and sometimes we don't WANT them to be art. But still, the controls are in the hand of the director and crew and, when desired, an artistic vision can come forth.
Games are like this only worse because you have to compete with the players desire to 'express' himself. The more 'art' you inject into your game of a significant level, the more restricted you are -- granted this is true for almost any gamer addition -- but art does not directly add to the game experience.
Everyone oozes over Passage. I think it's garbage. It's spoon fed symbolism with no actual "game". Why? It wanted to be art more than a game. It crafted it's artistic message and then, shoehorned a game in there. It's like cliche student art films that barely qualify as 'movies'.
Braid and SoTC were designed with no story in mind and no art inherent to the core concept. Jonathan Blow literally made Braid and phoned in for the art and plot (okay maybe not literally, but it was all done after the majority of the game was made). If you watch the early SOTC trailer, you see they clearly had no idea what they wanted to do, plotwise. They wanted you to kill giant, awesome things. They then crafted a beautiful story that fit into those confines, rather than fitting a game into the confines of the story.
and hell, sometimes games are just better as 'not art'. I liked Bunny Must Die a lot more than I liked Braid(not to diss on braid). It was awesome in ways that would not lend it's self well to being art, even though it and Braid were designed with the same base mechanical idea (time control). Jonathan Blow wanted something gentle and friendly that wanted to at least lend it's way to some nice, relaxing, artsy style (he just didn't care what it was yet). BMD gave you a cat girl in a bunny suit with a machinegun.
Besides, no one can agree to what 'significant art' is anyways. Being art is over rated -- and I'm an artist and game developer (IWBTG was totally not art)!
As for the art game I'd make... I'd make an art game meant to pander to the indy game jerkoffs who eat up the dribble that qualifies for 'art' to them and then have the ending rub it in their face -- that they got suckered in by a game with no purpose and meaning.