The video game is an arcade game.
And there was no separate comic series. But creator Ryan Brown was also a veteran of Mirage Studios and did some writing and character design for TMNT's Mirage continuity and a lot more for its Archie continuity before creating Wild West C.O.W.-Boys of Moo Mesa. And in the 2000s, when Mirage published Tales of the TMNT Volume 2 comics series, four of its issues were Moo Mesa crossovers written by Brown. Since he had always made other contributions for TMNT at Mirage over the years, these issues were technically still an in-house Mirage publication, but Moo Mesa and its characters are a separate copyright created by Brown himself.