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OpenArena used to be my go to FPS for impromptu LAN parties. Works on Mac, Windows, and Linux and it's easy to get a local server up and running. Plus it works great on ancient Thinkpads.

If you can get a modern remake of Quake I or II it would fit the bill. I have one on my USB memory stick that's forever been part of my keyring, just in case there ever is the need for a spontaneous fragfest.

Original Unreal Tournament is a pretty good one for this, I copied the install to a thumb drive on high school and played it on school computers all the time. Same with GZDoom