You absolutely don't need a degree to be a game developer. Having a degree will likely increase your chances to score a job interview, but won't guarantee a job in this field. Learning the modern programming languages is a must! C# and C++ are the top two computer languages being used by programmers today, from Indie to AAA.
Some people end up in game design by accident, while others sought it their whole life. There's no one way street to follow to this career.
Primarily I'm a programmer. But also do all sorts of work when needed. Including animations, level design, debugging, 3D modeling, etc...
If you become well established as a small independent game creator, you're free to focus on comfortable luxuries most jobs don't have. Including working in pajamas from your couch while watching TV, playing with your pet, and spending more time with your family.
I'm leaving this review from a professional indie developer perspective. There's a huge demand in the market. If you're a creative person with skills, you can accomplish a lot on your own, or with a well managed small team. You're free to work your own hours, and you can stop and go as you please.
While the perks make it a very tempting career to some, the truth is, you'll be spending the majority of your day in front of a computer screen. You're never really off while creating/marketing a game on your own, including a small team!
Learn programming! Lots of it.
Having a cool head, a sharp eye for detail, and a lot of patience.
It will always be in demand.