I don't think it is only for bragging rights, while in a vacuum the mainline kernel should be good enough for gaming, it is not really good when there are multiple tasks competing for the CPU attention (and this is especially bad for gaming because this can create a frame spike, ruining the game experience especially for multiplayer games). I think fixing this particular issue is one of the reasons Bore scheduler was created.

It's only fps bragging rights if you go from something like 180 to 190 fps. But for other person on slower hardware that may mean for example hitting consistent 60+ fps and eliminating stutter.

Or they lower the bar for someone that wishes to pick up Linux for gaming but are not comfortable or able to massage the distro it is based on into something gaming-compatible.

Not even close. An -rt kernel, scheduler, up to date MESA drivers and the like can make a distro much faster for modern games than a server-balanced one which is often set to yield a high I/O thorughput but bad multimedia performance.

Bazzite is the opposite of that.

The gaming version of cachy OS seems to come with default proton versions which seem to work around many windows kernel anti-cheat (valve proton being very limited as it seems).