Get that qualification if your current degree isn't closely applicable to advanced software development. A dedicated game development degree may be seen as being too "niche" for re-use somewhere else.
Game development is an extremely difficult field to get into for the major studios. For coding, you need to be extremely good, and be able to demonstrate that skill. Basically, it's one of the toughest coding jobs you can get into.
Get involved in online discussion forums relating game development (there's a great game development stack dedicated to this here ) with a view to increasing your understanding and communicating your learned knowledge.
Start developing ideas and code using appropriate development tools. Create your own mobile apps and see if you can get them approved and deployed to app stores. Having a good portfolio is a great step up and improves your learning and understanding of the field.
There's many books on this subject as well.
Game development is not fun. It's extremely hard work, very stressful, and doesn't come with huge pay packets, but does come with the chance of getting laid off quickly if the project doesn't succeed or runs over budget.
A lot of this work is offshored to the Asia or Eastern Europe where the labour is cheaper. You really don't get to sit in an air conditioned office in San Francisco. Play-testing is a myth, it's mostly automated.
I have a friend who's a QA director for one of the major publishers. I'm not making this stuff up to scare you, it really is that scary.