User blog comment:Deedlit11/Googology in Magic: the Gathering/@comment-5150073-20130412144609/@comment-5529393-20130413053425

There are a finite number of cards, but there are also tokens and counters, and there can be unlimited number of those, so there are an unlimited number of possible states. If you read the link, they actually simulate a 2-state, 18-symbol UTM, so to get arbitrary recursive functions you start with an arbitrary tape, which is constructed by having different creature tokens with different numbers of counters on them.

Why do you say that no programmable game can attain Turing completeness? There are other games which are Turing complete, like generalized minesweeper, Little Big Planet, etc.