The term "remaster" is definitely more applicable here. But when they state that you can reuse assets I feel like that doesn't mean you can reuse an entire game with minimal programmatic changes. Typically a game like this wouldn't fly in most jams, and it feels to me like this game wasn't made FOR THE JAM. I think people who make their game within the timeframe of the jam are more deserving of the prizes than a game that was made in a much larger time period than the jam allows with minimal changes added during the jam time.
EDIT: At the very least I would recommend adding a disclaimer to the top of the game's description that says it's a remaster of a game you've made prior to the jam. I believe it's misleading to not mention that this jam game had roots as another game before the jam.