I read this as implying that the loser is the one who makes the last mistake — the mistake that allows his opponent to win. But yeah, I think the quote is kinda sloppy — it assumes that the opponents take turns in making mistakes.

On a purely empirical level most amateur games once they reach critical positions are blunderfests punctuated by a few objectively strong moves that decide the game, and many complex positions near the end of games are similar blunderfests even among masters, and if you're assuming that the majority of moves are blunders then Tartakower's point is generally true. But I don't think that's what he meant.