Questions for the game owners:

Does local multiplayer work over a LAN, or hotseat?
Does local (LAN) multiplayer require accounts created?

Basically, I'd like to play w/ family on separate computers on LAN w/o having to create accounts for kids, etc. Thanks

Yes, there are both options. From what I gather there is also (maybe, I don't really know for sure) a mobile version (??) that can be played with the host if on the same wifi as well if you (I assume) purchase it. You can basically install on any number of your household computers to have up to 5 players. (I think, I wasn't really paying attention since I experimented at just after 1:30 in the morning PST)
In fact, it is compatible with those who have the Steam copy as well if they have the game on their Steam account. Hotseat exists but is called 'pass & play' which basically means the same thing. The same thing applies to the hotseat mode as it does LAN, 5 players max. (I think, I'll stand corrected if I'm wrong) LAN allows you to give yourself a local player name, so if you have multiple people who will hop onto each comp they can change the local player name to whatever they want within reason. The only thing I seen that requires an 3rd party account is the online portion of the game. (Maybe, idk 100% for sure. Looked that way to me, but I am willing to be proven wrong.)

But considering you were specifically asking if the local one comp/multiple comps required an account, outside of the GOG account you have that allows you to download the game, the short and simple answer is no. It does not require any account to be created outside of the account you have here on GOG.