When a card instructs an opponent to do something, how does that work in a multi-player game?
You choose an opponent. That opponent chooses a land for you to sacrifice.

At the beginning of your upkeep, unless you pay BlackBlackBlack, tap Demonic Hordes and sacrifice a land of an opponent's choice.

(You may choose a different opponent each upkeep that you do not pay BlackBlackBlack.)
From a 1995 ruling:

Choose a different opponent each time the effect applies.

(That link has a long list of such rulings for the cards that were available at the time)
For a more recent rules compilation, see
https://mtg.gamepedia.com/Multiplayer
According to the comments, theses are now in section 601.5a