I have heard about LAN yes and to be honest I am a little confused why you bring that up, the definition of a LAN has absolutley nothing to do with multiplayer and I never said otherwise, however you can play multiplayer on your computer (split screen), serial connection (in the old days), LAN (standar multiplayer) or by connecting to a server on the internet (often called online multiplayer), 3 of the 4 types I mention do not need a connection to the internet but they are all multiplayer. A multiplayer game is a game of several players not how it is connected together(Split screen, Serial, LAN or Internet)!
This is your very personal interpretation of what for today's standard is multiplayer...
I have an old DOS Monopoly game, it can be played with AI computer players or some friends can join-in and play too, I would never call this a Multiplayer game, not in the 90s, less so today :)
A good example of multiplayer space game (without SP) is EVE Online, the gamemakers must run a central server to administrate the players from all over the world (a costly exercice btw.). Such games also called MMO's (Massive Multiplayer Online) require online connection and an account just for the single reason (apart many others) that there are *rules* to obey if you join a multiplayer game, there are anti-cheating setups to follow, your chatting must obey strict rules etc. etc. all this cannot be done without account and online connection. And I'm not speaking about DRM here, nothing to do with it.
Instead, the game Elite: Dangerous is combining DRM with Single & Multiplayer. Here a online connection is part of DRM for the simple reason that essential game files are on the gamemaker's server and never will be entirely on your computer, no possibility to play offline...If you don't like online connection to play Single Player, well, you have to skip this game...
In GOG, look for the tags 'Single Player' and 'Multiplayer' to know what a game is about. In the Multiplayer case, there is a adequate menu in-game to setup your connection, but this is optional of course, as long as the the game is also Single Player this doesn't matter for you if you want to skip it.