The engine was written for Quake 3 by ID software, they're the makers of the Quake and Doom games.
Now that they have a more advanced engine (the doom 3 engine) they waived most of the copyright restrictions and published their code in a
Software Freedom Movement friendly way.
Now there is a handful of versions of the engine maintained by hobbyist projects. So, OpenArena isn't involved in the creation or maintenance of the engine at all. It uses one of the hobbyist engines and actually switched to a different one between this release and the last.
What ID didn't release was the game data: sounds, music, maps, textures, etc. Thats' where this project comes in, trying to recreate Quake 3 without running afoul of copyright.
I don't know about textures and models, but making Quake maps can be fun and isn't very hard. You should give it a whirl if you're interested.