"On the contrary...having a piece up in the right position is identical to placing the third X and then drawing a line through it. The rest of the game means nothing."
I don't see how it's identical. In Tic-Tac-Toe, if I remember correctly, the rules necessitate that the game will result in a win (even if played out all the way) -- the rules don't say anything about being up a piece in chess. The rest of the game does matter since some ways of playing a piece up will result in a win, others in a loss. It may not be interesting to some, but that's another matter.
So yeah I would agree to play on a Tic-Tac-Toe game where someone gets three is pointless, but I disagree that the analogy truly holds. No, I don't consider it "close enough."
"It is a clear statement that you believe your opponent is a dolt who cannot convert a clear win."
Just speaking for myself, I've played on positions without thinking my opponent was incapable at all -- I've even played till mate against master level players at times. That didn't make not resigning any riskier though, since if I lost as expected, it's still 0 points.