Does this version have the local co-op that the N64 version had? It states single player, but co-op local was part and parcel of the experience.

I know the Steam version DOES have splitscreen, 4 players. Hopefully GOG has it too, alongside lan!

Alright, I can confirm that Split Screen is still in the GOG version! But it doesn't seem to like Xbox One Controllers, only 360 Controllers.
EDIT: Nevermind, picking the "Local" Multiplayer option doesn't enable splitscreen. You do it via "Network" for some reason. PS4 Controllers work, so I guess XBOne Controllers whould work then.