Classics FPSes included Unreal Tournament 2004 and Quake 3. Both scale from 1 on 1 to 16 players well, meaning days of fun. Xonotic the open source clone, which is also very good
Worms is a hoot, can hotseat or LAN, armageddon I think the high point of the series. Hedgewars a more than worthy OS reimagining
RTSes are soo many, Warcraft 3, C&C series, or Total Annihilation all modded, all great. My choice is Balanced Annihilation or OpenRA for 2023 and OS
4X have classics like civ, but Stellaris a worthy choice too. Open source here includes unciv
Racing games are often a hoot too. You can get far too serious here if you want, but I recommend SuperTuxKart for some mariokart like action
Scorched3d another option for artillery fun. But generally Open Source all offer LAN gaming!