Hi bluesmoke, sorry I have only just seen this. This is not an easy task. However, since you asked: you would need to get the ioquake3 fork for Raspberry Pi out of github here
and go through each source code file comparing its differences to the original source here
which has moved on.
The goal would be to keep any changes that were made for portability to the Raspberry Pi and update it with the changes that have been incorporated into the original source since the Pi version was forked. I haven't actually had a proper look at it myself, it could be a huge job or it could be one or two files which have changed. If you go for it though, good luck
, you can still do Pi to Pi Open Arena multiplayer without having to do this. Doing the above would potentially allow you to play against other users who were running the game on PC etc.