ZDoom
A port (with enhancements) of the recently GPLed Doom/Doom II/Hexen/Heretic engine to 32-bit Windows.
It stores settings to an ini in its own directory, but is meant for multiple users.
If the username is Sally, every time it's launched by the Sally account, it uses an ini called zdoom-Sally.ini, if another account (let's call it John) uses it, it will use a different ini, zdoom-John.ini. Other than that, it seems portable.