It's actually worse than zero-sum for the players, because the house takes a cut. Usually the house takes about $200 off the table every hour (plus tips to the dealer), so the rake matters less for higher stakes games.

However, it's not necessarily true that half of all current players are losing. Because bad players will quit, it is possible that a majority of current players are taking money from a rotating minority group of losing players. I don't think that's true, but it's possible.