There is no informatoin yet regarding a game, but given that most games based on large budget films don't do well, I doubt Legendary will take the chance.
Creating a game based on Godzilla is INCREDIBLY difficult because of what he looks like, how he moves, what he can do, and all of the intricacies invovled with bringing such a creature to life within a realistic world without turning into another annoying and poorly constructed brawl game with bad graphics. I'll be honest, I have intensely disliked the Godzilla games like Godzilla: Save the Earth, Godzilla: Destroy All Monsters Melee, and Godzilla unleashed. They all had bad graphics, poor gameplay, and no story that hasn't been used to death already.
Making a game based on the new movie would be expensive, risky, and incredibly difficult. One thing that we all have to remember is that a game isn't a movie. There are many, MANY more limitations to what a game can accomplish compared to a movie. Again, I doubt Legendary will take the risk of making a game just because the movie did well. It's not a smart business choice to make a game based on one movie, even if it is a success.
