The game is strictly zero-sum, you win by bankrupting your opponents. The amount of money in circulation has nothing to do with whether it's zero sum or not, it's the distribution of money-- and in monopoly, the goal is to have it distributed to _one_ person.
P.S. Just because this also bothered me: inflation doesn't happen during the game. Land itself does not increase in value during the course of the game, it only increases with direct capital expenditures. Example: if no one buys "Park Place" for 90% of a game, it does not increase in cost the cost for the player who eventually buys it[1], that cost is fixed throughout the game.
[1] Despite its marginal utility (i.e. value) for each player increasing as the game goes on. In that example, it's nice because utility increase whether you have Broadway (I think thats the other piece) or not (preventing someone from building on it is a strategy too).