When you apply for a game programming job the company may have so many applicants that the first step for your Resume won't actually be with a programmer but a HR person or recruiter.
This recruiter will not be a programmer themselves, they may not know what C++, DirectX or OpenGL are. Or they may have a vague idea.
they will have a simple checklist that they follow to decide weather or not your Resume is worth passing on to a senior programmer. There could be thousands of Resumes for them to weed through so not having a degree will simply mean that yours goes straight in the trash without even being seen by a programmer or anybody who actually understands the stuff that you "know".

This is an oversimplification of how this stuff works and of course there are people on these boards that will argue that they got into the industry by knowing "stuff" instead of having a degree but, they are the exception to the rule.

There is no subject not worth knowing.

So much this, most especially for game design. Many of the best game designers have degrees in things like Philosophy, Psychology, History, etc. Even OP's example of Chemistry is a bit funny, considering there was a fairly popular indie game just released not too long ago called Space Chem. Which sold 230k copies from one Humble Bundle, nevermind how many other copies it's managed to sell, and the guy who wrote it was able to quit his job and go full time into game development.