There are several ways to approach this issue and not to depend on just the "illusion" and excitement of being part of Asgardia, because feels might fade with time.
The principal one is a crowd-sourced game like it was proposed, making the game escalable and renewable with the effort of people just because they want to participate in a game and make their little contribution. An updatable graphic motor, mechanics, models, and a grid-system to make a social based-game, or even a browser game or a RPG based on Asgardia itself would be awesome.
The second approach we should take in account is that we can crowdfund the game to a developer team formed /or not/ by asgardians. Being 500 thousand people, pledging 5$ each, plus random people that just wants to participate in the game, can become a huge amount that would be enough for making a stable game, and paying the developers for their effort.
The third approach is not to call it just an asgardian game. I mean, the game should be related to asgardia, as for the who makes it or what it will be about, but focusing on "hey, it's asgardian, just for us, our game", won't make it profitable and won't make asgardia's budget increase. Focusing asgardia's economy trade with earth by interchanging human intellectual abilities is a really good idea, and making games could be one of the many ways. So selling the game not by focusing the idea that it is just for Asgardia and a promotional thing, but a game alone made from people around here but that it is itself good by its own, may be the best way to make it profitable.