Yes, in theory. In practice, Github has become a hub for such living documents, especially in the Linux/OSS world, so it isn’t strange for people to look there for guides and recommendations.

I’m not opposed to it, but is there demand for it to be on GitHub?

There is! These sort of guides are best suited to be hosted at Github/lab because of their dynamic nature. Any recommendations and “best practice” today might easily become outdated tomorrow in this fast-moving Linux world! Plus you can have contributors too submitting corrections and updates (if you wish to merge 'em), so you’re not left alone doing all the work.

Here’s an example of one such guide I’ve used in the past that’s still being updated:

https://github.com/AdelKS/LinuxGamingGuide

Mini all-in-one PC are expensive, just buy a used/refurbished regular PC. If you want, you can get them in SFF (Small Form Factor), which are still upgradable and a better option than AIOs. Here are some results on eBay for reference.

I’d recommend getting AMD because of their excellent Linux support and overall better gaming performance. Also, you don’t need a dedicated GPU for playing old games, even more so since AMD’s integrated GPU is a lot better than Intel’s, and works better on Linux too.

But it you want to play current games, you’ll need a dedicated GPU, and that $250 budget isn’t going to cut it unfortunately. However, you always have the option of buying a cheap used GPU later on, when you’ve got some cash to spare. But for now, if you focus on older games then the integrated GPU on an AMD will do fine.