I think you're maybe thinking of blendOS, which is immutable Arch, but it's not specifically gaming focused. Afaik, there's no gaming-focused immutable Arch distros, excepting the obvious SteamOS.

If you really wanted to, you could install ostree on CachyOS, though I have no clue how you'd manage things like updates. PikaOS is based loosely on both CachyOS and Nobara, but it uses a Debian foundation, taking advantage of the same GitHub Actions that Bazzite uses; if one was so inclined, seems like you could roll your own immutable Arch gaming distro that way.