I've now been thinking about the multiplayer aspect of this. The first thing that comes to mind is something like DOSBox and Epic Pinball or other pinball games. Sure they'll have to take turns, but pinball is a fun time so the one who's playing learns the table and the one who's watching gets the spectacle. Going into the more piratey side of things, MAME or Retroarch. MAME especially has stuff like Marvel vs. Capcom, the Street Fighter series, Fantasy Zone... so basically, you can give them an arcade cab at home. And I'll mention FreeCiv again.

Back on the less-pirate side:

• Armagetron Advanced: Tron lightcycle game which can support local multiplayer. I've enjoyed it for years.
• Battle for Wesnoth: Hex-grid turn-based strategy (think Fire Emblem, Advance Wars, Final Fantasy Tactics, or Tactics Ogre). Supports local multiplayer.
• Any chess, checkers/droughts, or shogi game. I don't know if lichess or lishogi (both .orgs) support local multiplayer - but I know there are local ones like gnome-chess, brutalchess and gnushogi + Xshogi.

So there's my thoughts on local multiplayer games.