I work for a large game development studio.
If you didn't go to school, but you are energetic, disciplined and passionate, apply for QA roles and then commit to understanding the mechanics you see when you are testing. I know an Executive Producer of an extremely successful 2006 game that started in QA years before and absorbed the processes he saw around himself. He moved into design years later and applied this knowledge while absorbing process from the new disciplines around him. Then he was a respected Producer for years, mainly because he understood what it took to get things done in each area. Most recently he applied all of this with a talented team and made a great game.
Even young punks who think they know it all can grow up in QA. It is quite an eye-opener for these know-it-alls to be around disciplined, confident CompSci and other graduates who really do know their stuff. They often mature during this process can move onto roles with more responsibility. The ones that don't are easy to spot. If you have the education, the only thing that you need if you are missing experience in the games industry is modesty and passion. Modesty to work on the boring systems, and passion to make those seem exciting.
The industry really needs more candidates. If you see business news about the growing game industry, remember that 85%+ of that growth is people. We routinely hire talent from other countries because we don't get enough local resumes.
Statistics are no substitute for judgement. -- Henry Clay