Answer:
No.
A zero-sum game is a game in which players deal only with each other, and there is no way to gain "resources" outside of that.
There are squares such as "Chance", "Community Chest", Go, (and in some house-rules games, Free Parking) which give the player money. Obviously, this money does not come from another player, and is instead "created" on demand. This is what makes Monopoly a non-zero-sum game.