I suppose the problem is whether game designers even want their games to be interpreted.
speaking only for myself, i dont care if my work is viewed as art or not. one of my main concerns is if the people playing the game are enjoying it.
Right, I guess it depends if people are ready to accept "fun" as a quality of art as much as context as meaning. Music itself is really just a series of notes on a piece of paper, but the emotional effect of air vibrating in the pattern outlined in the sheet music is what counts as "art" in that context (and maybe the bad lyrics).
MW2 is a good example, because it plays very well and as mentioned, it also has a level that has some meaning. It's kind of poorly executed in hindsight in so much as there's very little context for your actions, but certainly it's a level that tries to make you realize the context of your actions.
You can have both, but very directors take the time to worry about storytelling in games (which isn't necessarily a bad thing, just a trend I've seen).