Why don't you try to see for yourself? Log on as a normal user, and try to play Doom3.
I don't believe you need to be an administrator in order to run Doom3, but with Windows nobody can be really sure, can he?
Anyway, as long as the game does not try to do something extraordinary (write settings to the registry while running, modify files in the game's installation directory), it should work ok. Just make sure that as a user you have access to the game's installation folder (both read and write). Same thing goes for the game's registry entries, if any exist.