Assuming that a degree is the only requirement (which is very unlikely, especially today) -> It depends on the company, but generally, in any place where developers make hiring decisions (which is where you actually want to work, for obvious reasons), your proven abilities are the only thing that truly matters.
Valve's Chet Faliszek makes that abundantly clear:
a degree isn't the only requirement anywhere but the idea that degrees don't matter to the extent that you are implying is just false and/or wishful thinking. There are a lot of truly great programmers in the world and 95+% of those guys have at least 4 year degrees, often from prestigious universities. You will be competing with them for jobs. Why would a hiring manager choose a great programmer who has no credentials over a great programmer with a CS degree, all things being equal? Because of the uncredentialed guy's obvious genius and the twinkle in his eye? -- this is fantasy, and doesn't even touch on the (social) connections a truly gifted programmer will make at a first-tier engineering school. Look, I'm not saying the whole pulling-ones-self-up-by-ones-bootstraps thing can't be done: just that success this way is much rarer and it is the much more difficult route. This is not the 1990's anymore and it is competitive out there. Telling a young person not to worry about college because game companies will just recognize how great they are is just giving really bad advice.
I see this a lot on these forums and elsewhere. I think there is also a belief among younger people posting here that the easiest route to success in the game industry or software in general is striking it rich on their own as an indie developer. Okay, this too is folly ... it's a nice dream and people should try and follow their dreams etc. But basically no one strikes it rich as an indie developer. If you're young and you want to write games the main way you are going to get to do it without having to have to do it when you get home as a hobby or a sort of second job is by becoming a real programmer and getting a real programming job for some game company, meaning becoming a software engineer, meaning studying engineering, period. It's really that simple.