This is probably the wrong place to ask, since most people around here are still in school, but here goes:
Neither job sounds like a long term situation, in that you will likely move on once you have more experience. I would be wary of the call center job because dealing with people all day is very, VERY high stress. The game management job seems like it would be more laid back, and would give you more free time. Since I'm assuming you don't want to be stuck in either of these jobs the rest of your life, I would take the game management job and use your free time to acquire skills that will qualify you for something better.
Since you mentioned you were interested in the game industry, there are a variety of possibilities: 2D art, 3D art, marketing, public relations, programming, etc. Pick a specialty, get good at it, and demonstrate your skills with a few personal projects. Add them to a portfolio, attach a resume, and then start applying for the bigger jobs in the industry so that you can fully support yourself and a family. Taking the call center job will pretty much leave you dead in the water until you save up enough to go back to school, which would be a positive outcome.