- The client/server network protocol and syncing state
- The VM architecture (e.g. most of the game can be compiled by LCC into a custom byte code and interpreted. This was for safely (although I wouldn't be as sure these days) distributing mods iirc. I think the main game was shipped compiled to x86 though. The interface between the VM and the core stuff is via "syscalls" and its fun to see how that's wired up.)
- The player physics/controls (i.e. walk/jump/collisions/etc.) (it's neat how fake first-person player physics always is. This isn't unique to quake 3 but quake 3 had notably good controls.)
It's a bit fun to trace what happens on 'w' keydown/keyup (when bound to walk forward.) When I first saw how that actually worked I was surprised (hint: it types commands invisibly into the command console ;) lots of string copies to do that.)