The PC version of Quake is very old, so if the Mac version is as old it'll run on pretty much anything. The PC version I think is a Dos application, and needs something called WinQuake (a Win32 version of the game that someone made) to even run on XP/Vista.
I recently got a copy of the Mac version of Quake I, which I'm going to try on my G3 - is there something like this that will add 3D acceleration with the Radeon? I have something called Tenebrae on my PC which makes Quake I OpenGL-accelerated with 1280x1024 resolution and everything and it's really cool, except one of the levels is broken and you have to skip it, I wondered if there's something similar for the Mac version?
Also where did you get the 1.09 patch from? All the links I could find for the Mac patch were broken.