tl;dr - Nolan confirmed that a game is in development set in the Inception unvierse, but that it will not be the events of the movie.
I'm thinking that it would be ideal for an RPG/TPS, possibly cribbing elements from Echochrome. It would be really sweet if you played each level of a multilayer dream, where the highest level would be played for 30 seconds, then you would play the next level for 10 minutes. The 30 second top layer would generate a "track" of modifications and warping to the subsequent layer, i.e. you're in a car and your swerving, this results in gravity going wonky in the lower level of the dream at the corresponding times.
The other main wrench thrown into the formula would be the ability to manipulate levels if it was your dream, something only briefly touched on in the film. Echochrome is a great little game with some similar concepts, where the geometry of the level changes based on the perspective you shift the camera to.
But I have a sinking feeling it's going to be a completely linear shooter to appeal to the dudebro crowd with predefined setpieces. Inception was already pretty video-gamey to begin with. It already has an in-universe justification for the endlessly respawning mooks that all look the same
