Klinefelter syndrome does not make the male a woman. They are still male. Triple XXX syndrome does not make a woman male, you need a Y chromosone for that.
So yes, they still fit into two categories.
Klinefelter can result in the sexual features of women developing, specifically increased breast tissues, giving someone with male chromosomes the appearance of a woman.
But here you are doing exactly what I suggested you would originally. You spoke of XY or X. The spirit of that is that men are XY, women are XX, no variation, no diversity. But there quite clearly is.
Even if we go with your "I said Xs and Ys! That still counts as same!" and dismiss those two, there are other disorders of sex development that prove your initial assertions ("The human race isn't diverse. There's those with X & Y chromosomes and those with X chromosomes ... Chromosomes don't lie.") wrong even if only one person had each condition.
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