Inception was a 2010 movie where the audience became submerged in the land of the dreams, travelling into the subconscious. Director Chris Nolan was hesitant about making a sequel, but was more receptive to a video game. The company that I think, is well suited for the job is, Quantic Dream.
Quantic Dream worked on the hit, Heavy Rain, which made people interested in the story as well as the game, leading to a movie possibly in the works. The game was about human nature. Even the name Quantic Dream fits Inception! They also worked on a short film called Kara, and won the audience's attention and empathy. Currently, they're working on the video game, Beyond, with Ellen Page, similar to Inception, but it deals with afterlife instead of dreams.
Quantic Dream gets the players involved in the game, and very attached to the characters. In Inception, the game should have four to five characters, like in Heavy Rain. The extractor, the point man, the forger, the architect and the chemist. I think this could work better than the film. It would have intricate mazes and traps; it would be interesting to see an elaborate city made in someone's dreams, inhabited by the subconscious.
The gameplay would be intense, like when Arthur was in the antigravity hotel. You'll be able to fight projections and the level of difficulty will increase with each deeper dream level. The realistic nature of the animation Quantic Dream uses would make this a vivid and really cool game visually. Usually in video games, when the player finishes the game, the game ends. With Inception, there should be some puzzles, like DLCs, that the player can add to enhance and continue their game-playing.
Nolan said when he imagined an Inception video game, he saw a whole world where Inception was possible, so this opens it up to a completely new story and fresh cast. However, some references to Inception, the movie, like Cobol Engineering, or a mention of Cobb or Arthur.