If you're really open to anything I have found that programmers and artists are nearly always in demand in the game industry. Programming nearly always requires a computer science degree to really have the foundations you need. It's less important in art, but you have to be really, really good to get by just on 2D non-digital art skills these days, so an education there to learn the software is also probably a good idea. There are aspects of video game art that aren't as dependent on how well you can draw a monster or hero: say animation or tech art.
Riot, like many studios, hires a wide variety of people necessary to keep the business running that aren't strictly speaking working on game development. We have massive IT needs. We host events. We have finance and legal departments. Generally all of those positions require a good education as well. At Riot in particular, you'd need to be a gamer to really fit into the culture. That might not be the case at every game studio... though you may also want to ask that studio why that isn't the case. :)
It can be hard to break into this industry with no experience. Internships are a great source of experience, though those can be hard to snag as well. These days it's easier than ever to work on an independent or small team game project with all of the free engines and tools floating around. In terms of game design, since that is the field I am most qualified to speak about, we look for people who can finish projects more than people who have great ideas.
Our studio is headquartered in LA, though we do have other offices. We are able to relocate people for a lot of the kinds of positions that it sounds like you'd be interested in. Southern California, Washington state, Texas and a few spots on the East Coast are clusters of game development within the US.
Also remember that making games isn't the same thing as loving to play games. There is a ton of overlap of course, and while I wouldn't trade this career for anything personally, it is very hard work. Not every person who loves great restaurants would really enjoy being a chef. :)
The good news is that this industry is still growing and most of the people I have known who really wanted to get into making games were eventually able to do so.
Best of luck!
