CachyOS claims performance improvement by compiling its packages with CPU-family-specific optimizations. Okay, but most games are not CPU bound, and even those that are mostly spend their CPU time in game code, not distro package-provided code.
CachyOS claims interactivity improvement by using the BORE scheduler. Okay, but that's unlikely to help games unless you're running other tasks that compete for CPU time while you play.
So for most gamers, I wouldn't expect CachyOS to offer much improvement in either area.