Is it possible to stream movies via old version of iTunes (iMac G4) on Apple TV 3 or is the latest version needed?
http://support.apple.com/kb/HT4437 says iTunes 10.2 or later is required.
If your iMac G4 can run OS X 10.5 (Leopard) you should be able to run iTunes 10.3.1 (http://support.apple.com/kb/DL1103) which qualifies.
If it can only run OS X 10.4 it appears that the latest version is iTunes 9.2.1 (https://discussions.apple.com/thread/4108495?start=0&tstart=0) which does not qualify.
Note that I have not verified the above. Also, based on personal experience, you want as good a network connection between the source and the AppleTV as possible. Either cabled or 11n wireless.