Baldur’s Gate 3 is the obvious suggestion at the moment. That and Civ 5 are both good if your group wants something at a slower pace. For a FPS, I highly recommend Star Wars Jedi Knight: Jedi Academy. Your players might be surprised at how good it feels even today.

StarCraft is a solid pick if you’ll have an audience.

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!

Lethal Company, a PC game, is currently hitting the charts. It’s a horror game kinda where you have to find scrap metal. It’s got some of the best AI enemies and they make it a challenge. I think it supports LAN but it’s not tagged in Steam.

Surprisingly, I don’t think Terraria has been mentioned yet. Dedicated server can be downloaded for free and fun on Windows or Linux. I’m relatively sure that even spontaneous hosted games (from inside the game) are LAN accessible directly.

With Goldberg Emulator you can play a lot of online games on LAN from Steam:

Steam emulator for GNU/Linux and Windows that emulates steam online features. Lets you play games that use the steam multiplayer apis on a LAN without steam or an internet connection.

https://mr_goldberg.gitlab.io/goldberg_emulator/

I used it a long time ago, but it always worked flawlessly.