Arch rolling gives up to date packages quickly. The most important part for Linux gaming is quickest pushing of GPU and performance related kernel code, so that the most optimal balance between battery life and performance is continuously achieved, because Linux gaming is still in its infancy. Every new update or package possibly giving this benefit matters to Valve, and they need maximum amount of time to optimise and push updates.
There is no GNOME hate angle, unlike what a lot of idiots here want to claim and spread the toxicity for it. KDE people, Snap haters, systemd haters are extremely vile people. Valve does not care about working with UI, since they can design a launcher for any Linux distro themselves, hiding the ugly terminal and filesystem well enough for casual gamers.