The statement does not work as a universal truth. There are times when teams win because of their running back. Adrian Peterson is a big reason the Washington Redskins even sniffed .500 last season.
But the statement isn’t completely literal. It’s a quaint paraphrase job of the data-backed revelation that teams who build their offenses around the run game are inherently less efficient than teams who build their offenses around the passing game. The versatility of the passing game, especially with play action, is the way of the future, and some teams haven’t caught on yet.