Well, hanging material definitely isn't the ONLY way to lose a game, so not EVERY game ends that way. For example I would contend that in this position:
The move 1. Rb7 does not hang any material. It certainly loses though.
A similar case of a losing move that doesn't hang material might be 1. Kb1 in the following position:
If you really want to parse semantics, though, perhaps you might argue that those moves "hang the king" by allowing mate (immediately in the first case, slower but no less forced in the second). If you're that much of a nitpicker, allow me to offer one final way a game can end with no material hung: resignation. It's entirely possible for a player to misevaluate a position AS losing, when it's actually not, and resign. That player DEFINITELY would have just lost a game without hanging any material. We've all had this happen to us, right? At least in blitz? Whether it's you or your opponent that benefited, someone plays a tactical shot that looks crushing, the other player can't find a way out and resigns, and then afterward you find there was a resource that totally thwarts the "tactic"?
And of course there's one more obvious option: the clock. I'm pretty sure that at some point in chess history, someone has probably flagged and lost in a game where they had not at any prior point hung any material.