Is switching my major to SGD worth it, or should I stick to getting an associates in arts or science?
Liberal arts degrees are mostly worthless. Go for math and science, and learn to code. Some of the former "game developers" I talk with are now app/software devs working in areas that pay well more.
Swaggermuffin is absolutely correct.
However some minor other observations ; for many jobs all that matter is you have *any degree at all*!
A degree is a resume filter for some businesses. When they have 100 resumes to review they go through and say "which ones have degrees? throw the ones that don't in the trash!" Look now we only have to review 12 resumes!
Sure; there are fields where experience or demonstrated ability to produce real output is more important than a degree -- but there are many more that literally do not care what your degree is in, they just want to hire someone with a degree.
So if that's all you care about then get whatever degree is easiest or most pleasurable to you.
However if you really care about what your going to be doing with the rest of your life; and you'd like that to be in either programming or even specifically game design and creation -- then absolutely get a computer programming / science style degree hands down.
Also make things that you can show that its not just a piece of paper.
In the end you may not get to make games professionally - but you almost certainly will get a great career in the tech industry that pays well.