Didn't know about that clone, thanks.

Hey.

Initially I wanted to recommend Wolfenstein: Enemy Territiry, but then I noticed: more or less no real-life guns + agression.

I believe you should check 2 games from Star Wars series: Jedi Knight: Jedi Outcast 2 or Jedi Knight: Jedi Academy.
If i am correct, they have LAN option. + Probably they were designed up to 32 players in mind.
Additionaly - it's Star Wars + lightsaber combat. What is NOT to like?

Beyond above suggestions, Stardew Valley supports up to 8 on PC.

I would recommend OpenTTD as well, I know it's not appealing to most players, but it's non violent and can be considered educational. Besides being free, it's the most hassle free LAN game experience I ever had with any game.

OpenTTD allows 255 players to connect, however, the limit is 15 companies (i.e., some would need to share companies).

It works on Windows, Linux, MacOSX, Android, whatever else it runs and they all connect to each other on LAN without complaining (as long as they share the same version number).
I remember I have played a few free Quake-based FPS, for instance, Smokin' Guns, but it breaks on new OSes for some reason. OpenTTD never failed me.
It doesn't matter if you are running a high-end PC or a potato tablet, Windows XP though Windows 11. Linux 3 through 6, Android 2.2 though 12 and so on. Even if the OS is stuck on Safe Mode/Failsafe boot, or if it uses Desktop or Server Kernel.... and again... they all connect to each other on LAN without complaining (as long as they share the same version number).
Just don't try hosting very large maps, because it would take time to connect and might cause drop outs.

And... even if it causes a disconnection... anyone can reconnect at any time without losing their game. You don't need to be stuck on lobbies waiting for everyone to be ready to start or restart if anyone disconnects. Even if you want to, it allows to save and restore multiplayer games. It also autosaves frequently.

It is also on GOG but I recommend browsing their website to get an updated version, or an older version if you need to find a specific version that runs on every device you have.

One more vote towards HedgeWars, free and a lot of fun.

Racing games that are not dificult to playare a good option:

Trackmania Nations Forever is available for free through the website ("You can download the free game by clicking here"). It's a time trial racing game, when played LAN one can race against other player ghost, had lots of fun back in the day. Played with only 4 buttons.

On GOG there's also https://www.gog.com/en/game/flatout_2, not sure how many players it supports at once (at least 4) and there's plenty of modes to have some fun, including "Destruction Derbi" mode, where all cars drop in a arena and smash each other until only 1 stands. Also very easy to play with only 4+1 buttons.

There's plenty of strategy titles that fit your requirements but they are usually time consuming to learn, not really well suited to a class. That said I recomend the free game Battle For Wesnoth or on GOG Age of Wonders Shadow Magic, Heroes of Might and Magic 3 or Civ 4.

If I correctly remember Terraria also support LAN but unlike other games listed, I didn't play Terraria on
LAN. It's sort of a 2D Minecraft.

Not on GOG but also great to play on LAN is Age of Empires 2, there's "Definitive Edition" on Steam still updated to this day, that recently got the price increased from 19.99 to 32.99 (probably will connect via Steam API), but the Gold Edition (quite old) was available DRM-free, so you could install on many PC's without issue. You many need to hunt a old CD though.
It's a historical competitive RTS that can double as a IT and History lesson. As far as I know the max number of players is 8 and can be configured to solo, teams or alliances.

Edit: Pertinent list created by GOG comunity

Edit n2: Streets of Rogue is not only a amazing game, it also supports LAN.

As a bonus, it's open source, so maybe they could crack into giving it an update or you know, adding something to it.

Just a side note, this might not beat the suggestions of OpenTTD and Hedgewars,

However, if the students already know how to play Minecraft, you can try Luanti/Minetest, https://www.luanti.org/
It is pretty much a free clone of Minecraft but less resource intensive; it also allows to create larger maps but that wouldn't help much in your case. Creating mods are usually easy and very educational as well.
It also allows to reconnect at any time and you don't need to wait in lobbies.