The cat seems to be very omniscient. He also seems to be very mad. Both of those combined allow him to know about his fictional nature without getting a breakdown or something. He knows about the fourth wall, and he probably knows more about its cracks than anyone else.
But I think he knows even more than that. If he is indeed the Cheshire Cat from Alice in Wonderland, then it would be very in-character for him if he knew about the ARG. As in, he would know that all this is just a game.
I sincerely hope I have blown your minds. Please discuss
(if he reads this, it won't matter much, because he's mad anyways)