Since it sounds like they are going to put this game in their real game as a mini-game, I can understand the strictness here. It would be lame if this was a free form hackathon, but really it is just a porting contest for producing an easter egg to put in their real game. It would be pretty strange legally to have someone else owning a game in their game.
It would not be even a tiny bit strange. Games almost always ship full of code that belongs to other people. Think about middleware (e.g. Bink codecs).
The obvious thing to do is that you're only eligible for the contest if you grant the contest-holders appropriate (non-exclusive) rights.