Insufficient material
Ok, what "insufficent material" means is that the player with more pieces ran out of time. Now, normally, when a player runs out of time, they lose, but, if the player who still has time on their clock doesn't have enough pieces left to checkmate with (like, only a king), than the game is ruled a draw, and the player who ran out of time does not lose.
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In a recent game I was reduced to just my King and my openent was racing to get his pawns home to make new queens. His time ran out and the games was declared a draw.
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You cannot checkmate, you cannot win.
The point we're all trying to make is that it's not JUST a "race against time" as you call it. In order to win a chess game, you MUST reatin enough pieces to be able to checkmate. If you don't then the best result you can hope for is a draw. I don't know when that rule was first worded like that, but I'd venture to guess that it's been this way for around as long as clocks have been used in the game.