Managed to get it working. Here's what I did:
1) Install Q3A in classic. Make sure it plays.
2) Move the quake3 folder from the root of the drive over to the apps folder
3) Copy the *entire* contents of the baseq3 folder from the CD to the same folder on the quake3 folder on the hard drive
4) Maske sure it all still plays.
5) Go
here and download the patch.
6) install the patch.
7) It will have installed a 10.1 directory inside your /applications/quake3 folder
8) Inside that folder, there should be Quake3 and Quake3 G4
9) Launch the appropriate icon.