just like
the spirit of the game is superior to whatever the current rules are.

This is a very meaningful observation: there is indeed the spirit of
the game, and I think in a drawn position with clocks roughly equal,
say a minute or so each to go in a blitz game, a draw would be "the
right thing." Surely a legitimate cause of complaint, in terms of
sportsmanship, would be in such a situation to merely turn the contest
into who can click the mouse (or punch the clock) faster, over a
series of dozens of moves.

I am convinced now that in my case, which was a tournament game, my
claim to a win is easily justified by my markedly better time
management. Thanks to everyone who responded and clarified more than
just the letter of the law.