ioquake3 runs quite nicely on my Pinebook Pro with Panfrost.
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You need to copy your original Quake III files from a PC installation in order to run Q3A.
Set the COPYDIR variable in the shell to be where you installed Quake 3 to. By default it will be /usr/local/games/quake3 if you haven't set it. This is the path as used by the original Linux Q3 installer and subsequent point releases.
Run 'make copyfiles'.
cd into your Quake III directory and run it:
DBUS_FATAL_WARNINGS=0 ./ioquake3.aarch64 +set cl_renderer opengl1 +set r_mode -1 +set r_customwidth 1920 +set r_customheight 1080 +set r_fullscreen 1 +set cg_drawFPS 1