As I am a Muslim, does Islam encourage me to contribute (money and code) to open source software or games?
You are free to price your buissness according to Islam, as long as it isn't exageration. I am a software developer too and design software free as well as priced. If your contribute money to a good service for people like code then giving some part off as open source is encourageable in terms of spreading knowledge.
If a game is oriented towards islam like quiz or such i.e, complying with the terms of sharia then you are encouraged to help it and earn the reward of sharing knowledge. If it is not sharia compliant then I would suggest to stay away from it, that would be better for you and others.