Most of the time video game designers are trying to make 3 dimensional virtual worlds that are as realistic as possible, or focus upon a particular art style, and tell a story within that world.
What I would like to see is a lifelike 3-D world that has a main character that has special abilities, or levels, taken from modern art. This means, for example, that a character with Cubist special abilities (or in the cubist level) can flatten parts of the world that they are looking at into a 2-D space, but in this space they have the ability to see around corners, rearrange objects and do all the other funky things that happen in cubist art.
On the flip-side, when using the Cubist skills, the character would lose depth perception, motion would be funky, and other sorts of strange phenomena would go on.
Moreover the character could get skills associated with other artists or artistic movements. Say there was a Dali gun: it could stretch the legs of elephants (or any other animal) such that they become unstable. Or a Duchamp Readymade skill which combines random objects in the world into other objects depending upon the angle at which you are looking at them. Frankly I think that there are too many different and good ways to go; it would take some effort to really take a few ideas and make them work well.
This would be a great way to combine the ‘new’ media form of interactive video gaming and more ‘traditional’ modern art. It might even be considered educational. But if executed well, it would definitely be fun, interesting and visually impressive.