Unfortunately, I'm pretty sure there is no cat eating. :)

The show started out as more of an adult oriented comedy but the character became popular with kids. After the first season they toned down the adult humor, direct references to eating cats and things like ALF drinking beer. The Wikipedia entry for the show mentions that there was a case of a kid putting the family cat in the microwave after watching the show.

I'd love to see this game remade and greatly expanded as an adventure game using the SCUMM engine. It should definitely include the ability to eat cats.