I was going to suggest this game as well.
You get an overhead world map like with locations (places, villages, and cities) and an opponent.
You can enter individual locations and take them over, you need to clear out hostile combatants and talk others into joining you.
You collect items and can build better weapons, water pumps, or I think trade things that other people had. I remember it was very luck-based as to whether you’d get useful items. Sometimes you just had to give up and restart.
I think if you take over all of the locations around a city, then you can take over the city too. If you take over all the cities then you win. However I never used this method. It was very long and also some of the locations are radioactive so it’s difficult to go there without dying.
The other way to win is to wait until the opponent is at the end of a map path where they can’t circle around to a city, then take over all locations along that path so your followers block the opponent from hunting food or getting water. Eventually the opponent starves to death and you win.
I’ve read that the 1993 Amiga version featured the opponent as a character you could actually meet in a village and fight. That was removed for the 1994 DOS version, presumably because hiring some muscle and making a beeline for the opponent could result in some very quick wins.
Max Design GmbH generally made strategy/management games with much larger scope than this (1869, Motor City, The Clue) but Burntime is surprisingly compact.
From what I understand there’s hotseat multiplayer as well?