TLDR: owners of a copyright (R&M), have to sue unauthorized productions or they will lose the copyrights to the public domain.

Because the people who own the rights to the copyrights would sue the video game creators unless the video game creators paid money/made a contract. The owners of the show don’t have a choice, if they don’t use and protect their copyrights then they technically lose them and the product becomes free to the public domain (like music from 1902). However this all seems a little ironic considering the two main characters are directly based on the characters within a certain movie franchise about time travel. The reason it is legal to make the cartoon is because the show does not impersonate the movie characters, they emulate them. Emulation vs impersonation and a few other reasons.