Universal Studios: Theme Park Adventure was a game for the Nintendo Gamecube console, released around 2002. It sold poorly, however included a Back to the Future: The Ride mini-game which allowed the player to control the DeLorean time machine and bump the other DeLorean stolen by Biff Tannen as many times as possible within the time limit to force him back to the present.
The time periods encountered are the same as the ride: