Mathematically, you're correct that it isn't necessarily true that half of all current players are losing. It isn't even necessarily true if the pool of players is fixed, since the game being zero-sum doesn't constrain the possible distributions of winners and losers very much. The reality, though, is that the vast majority of players are losing.
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.