It's impossible to say what difference those 35 points made to the game- you can't start second-guessing about the sensitive depenence on initial conditions.
By virtue of this thread's existence you obviously did not intend to cheat the other player, then this should be written off as no more than a basic rules error that ocurred in-game.
If you feel guilty about taking the prize as a result of your error, then you should compensate the runner-up for their entry fee, or else half the value of your first-place prize. That's what I would do.
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