"Set up" means that the cat is really who rearranged your living room, but he made it look like the dog did it. He "set him up", or "framed" him to make him look guilty of a crime he did not commit.

Set up has a couple of meanings: : the process of making something (such as a machine or computer program) ready to be used : the way that something is done or organized : a situation in which someone is deliberately put in a bad position or made to look guilty In this instance, "Maybe he was set up by the cat", it would be the third meaning (to make someone look guilty). I guess the cat made the dog look guilty.