Doubt it. I would figure their computer system puts a random number on the card, and the door scanners send that random number to some server, which tells the door whether to unlock. The card might also contain just a code unique to that door and a time for when it works, but that would be too easy to hack and not very flexible - you might want to cancel a card early, or extend it, or cancel and issue a new one, which would be hard to do like that.
Either way, putting the credit card number on the cards just doesn't make much sense.