From their site:
OpenAI is a non-profit artificial intelligence research company. Our goal is to advance digital intelligence in the way that is most likely to benefit humanity as a whole, unconstrained by a need to generate financial return.
The money quote is at the end, literally—$1B in committed funding from some of the usual suspects.
Being a billionaire is evidence more of determination than of luck. I also don't think billionaires believe they are the smartest people in the world. But like everyone else, they have too much faith in their own opinions when it comes to areas in which they're not experts. They just get listened to more.