My understanding is that there are basically two ways in which a game of chess is won.
(1) One side gives (or forces) checkmate, regardless of material situation on the board. He may be in material inferiority, but mate is unavoidable.
(2) One side achieves enough material (or positional) superiority that with correct play will inevitably lead to a material advantage (if superiority was positional) won endgame and then checkmate, although at this stage mate is hardly forced. But the other side, for reasons above explained, resigns.
Am I missing something? Are there a 3rd, and maybe even a 4th, case (not considering forfeits, illegal moves, and so on...), in which a game is won?