Back in the old days, you would setup a LAN and a server or someone would host the server on their own machine and you would all play.  No internet connection required...  LAN gaming isn't dead, it is just that most people don't want to take the time to setup a home network and play.  Linux has some decent games that can be hosted in a LAN environment.  Another option is to host a dedicated Linux server for something like Counterstrike (pre-Steam)

https://www.reddit.com/r/linux_gaming/comments/2mjnod/what_are_some_cool_linux_games_suitable_for_a_lan/