Both Quake3e and ioquake3 are engines, but not the game. To play, you still need pak0.pk3 file which is not free. It is included if you buy the game. Bethesda [1], GOG [2], Steam [3].
Open Arena is an open source shooter based on the original open source quake 3 engine that you can play without licensing the original creative work: https://en.wikipedia.org/wiki/OpenArena