I’m not familiar with the situation, but I imagine if Southpark went around suing people for using their stuff, people wouldn’t take them seriously. Virtually everything in Southpark relies on their abuse of Fair Use. Just because it IS infringement, doesn’t mean you have to sue them.
It looks like there are a few other tracks that Bobby Prince is responsible for that made it into Doom. In this interview he states that he made them for fun, labeled the files to not be used in the final game, and was surprised id even had copies. When Romero made the decision to include them in the game, Bobby (who is/was a lawyer apparently) says he was sure they would get sued.