A good setting for the game would be Cobb’s (or just about anyone’s, for that matter) earliest years working as an extractor. In fact, it would probably be even more interesting to see Miles’ early years. Following him as he discovers the powers of the mind gives good excuse for the leveling-up/power-gaining process of the game.
I think the game itself would probably work best as an action rpg similar to Mass Effect. You would play through missions in the real world and in the dream world. In the real world you would do the bulk of the rpg elements; talking to people, learning information, and the occasional gunfight or chase. Those areas would function like a traditional game. In the dream world, however, is when you get interesting abilities and scenarios. You would also have two main meters to keep track of. The first would of course be your health, and the second would be something along the lines of a “hostility meter”. As Cobb explained in the movie, the more changes you make, the more hostile the mind you’re in becomes to you. So you could, for example, erase a building in order to make a shortcut, but you would start to face more enemies.
Also, since you get to invade many different minds, you have to play by the rules of their minds to fit in better and evade notice, so you’d get to play in many different styles, each appropriate for the character. And of course then you get into races against the clock before the kick comes in layered dreams and such, but that’ll take some more thought…