MacDorman isn’t splitting hairs with this analysis. It’s right there in the second paragraph of Turing’s landmark 1950 paper, “Computing Machinery and Intelligence,” published in 1950 in the journal Mind. He begins by describing a scenario where a man and a woman would both try to convince the remote, unseen interrogator that they are female, using type-written responses or by speaking through an intermediary. The real action, however, comes when the man in replaced by a machine. “Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman?” asks Turing.
Something that doesn't get mentioned enough in these discussions is that when Turing came up with his "test" (actually just a part of a groundbreaking paper on artificial intelligence) he was being forced to imitate a straight male. The notion of gender was much more central to Turing's ideas of identity than it was to intelligence... and so was the test.