specs? you can configure alot of things inside these servers.
but if you use dedicated servers without graphics you can run a game server on almost anything. Only bots use alot of cpu time.
anything that has any AI whatsoever takes up cpu power. Those nazi zombies of yours also need some AI so yes.
You can run a server game from the normal user interface (just start up the game normally and host your own server). But then you'll need a graphics card to even start the game. Most games also have dedicated (command line) servers where you won't have a normal user interface.
I know UT 2004 has a free dedicated server you can download. Try that.