You're right that the online multiplayer portions of some GOG games *do* require individual license keys - so yes, even they aren't 100% DRM-free for all functionality. But yes, they *do* get out of the web installer thing, and yes, it increases the file size of the installer considerably. It's a trade-off, with no cut-and-dry solution.
The pre-packaged requised files are fine to get the game running indeed. They are however, generally outdated so not recommended. You'd have the game running, but you'd still have the need to update online ASAP. Not really an advantage therefore as you'll need internet connection anyways to download a game..
Apparently registering Don't Starve with Klei is completely optional, so that makes it DRM-free unless GOG is lying. Monaco also has a LAN multiplayer mode which doesn't require Steam at all.
Completely? Not really. Sure, you can play an outdated version like the other games have as well, but GoG compared to Steam is at least weeks to months behind on pathes and updates in general and not just for recent games. Same to a lesser extent is true for Desura compared to Steam, mind. GoG is not lying about you being able to play the game without it, but then again nor are EA, Ubisoft, Rockstar, 2K and just about any other company around. Can play? Yes. Can play the full, updated game '100% offline'? Hardly ever.
LAN requires no access at all to the internet, Steam or otherwise. You just need 2 users with close to identical copies of the client software and compatible and connected hardware.
If it's a major update behind, it often will not work, let alone be missing content. Steamworks multiplayer is online MP though and hasn't really got anything to do with local co-op/MP. True local co-op aka 'hot-seat' gaming goes further in only needing the game to support it and perhaps adding a controller or so.