What do you mean with “boot into game mode” ?
CachyOS
Which is intended for handhelds, and explicitly marked as experimental and it is explicitly stated you can expect broken things: Readme.
It also has firmware and quirks for several handheld gaming consoles.
This edition is not intended for desktops and not tailored for them.
It is for handhelds…
Well, what exactly do you desire here?
The gamemode stuff can be installed with:
sudo pacman -S gamemode
The scx schedulers can be installed with:
sudo pacman -S scx-scheds
and started with e.g.:
sudo scx_lavd
Available are currently:
scx_bpfland scx_flash scx_lavd scx_loader scx_pair scx_rlfifo scx_rusty scx_userland
scx_central scx_flatcg scx_layered scx_nest scx_qmap scx_rustland scx_simple
More info here.
You can also make them autostart via systemd units.