[Veedrac]

I don't think that's correct.

> a man (A), a woman (B), and an interrogator (C)

> The object of the game for the interrogator is to determine which of the other two is the man and which is the woman.

> The object of the game for the third player (B) is to help the interrogator.

> We now ask the question, ‘What will happen when a machine takes the part of A in this game?’

So the machine is taking the part of A, which means that there's a machine and a woman. The interrogator wants to know which is the machine and which is the woman, the machine wants to deceive them, and the woman wants to help the interrogator figure it out.

Of course it is plainly obvious both as presented by the paper and by basic inference from symmetries that gender was only relevant for the introductory example and not after the machine took place of A.