Many of these distributions, at least the popular ones, are nothing more than forks of Debian, Ubuntu and RHEL/SuSE. And most (not all) people who would want to game on a Linux system use Ubuntu as it's by far the most painless thing to get going. Base yourself off of the latest Ubuntu LTS, compile your project statically as far as possible and you're probably good to go, containers can be used to get your project running on other distros if needed.

If you're using any engine even better, all of the major ones are cross-platform anyway and abstract all the nastiness away.