From my 2 seconds of experience in developing games, I think out of the web dev languages, javascript would probably be the more translatable to being a programmer in gaming. The drawing and 3d modeling are definitely useful, and the overall understanding of laying out screens and designing screens are also useful. There's so many different parts to a game development team though, so don't feel like you have to be some expert programmer to contribute.
See, the people counseling me are advising against it because I'm terrible at math. But I was thinking the same thing: If I'm on a team, which is like a 95% possibility, why would I be expected to be a 1 man team all wrapped up in one? It's not realistic, and there's not a whole lot of people who have the skills to program games as it is.