A decent source for the spread of Linux OS's is:
https://distrowatch.com/ find on the right of the main page, currently.
Of course this is a different data set - hits per day on a web site, so
interest in particular operating systems. I have seen similar figures in Reddit what Linux OS do you use survey/polls (too lazy to check at the moment) so in the big picture it's pretty accurate. Pretty sure that of the top 10 (at this moment) only Mint and Ubuntu (and maybe Zorin?) are Ubuntu based.
The spread of gamers over this set is another question and I suspect that leans more heavily toward Ubuntu since many game players migrating from Windows are likely to land there (or Mint) at least as a first point of call.
I think one of the factors for Valve when embarking on SteamOS was potential use/popularity of the system (=Ubuntu based, hopefully being able to handle Debian). That they introduced it leads me to suspect that they think a decent sized market exists.
In terms of pure gaming speed Arch might be the best Linux OS for gaming especially if configured as a stripped down lightweight (only what is necessary) version. Probably not something for the faint hearted to jump right into though. However there are a number of specific gaming Linux OS's that I have no knowledge of beyond the fact that they exist.
On a different tangent, I find it interesting that it is generally the small to mid-level developers who are prepared to support multiple platforms.