My guess is NASA is trying to reach younger crowds & they did this as joint marketing campaign. More kids get excited about NASA & space while Rovio gets even more press and coverage for their new game. Everybody wins.

Surely they paid for it? If so, is the the first use of private advertising on the ISS?

It seems like that would be really, really expensive unless NASA actually wanted to help them out. I think it's mutually beneficial NASA is trying to reach a younger generation as they struggle to stay relevant given that they don't even have a human launch platform ATM.