Turing did introduce the concept of the game by having it played between a human man and human woman, with the man pretending to be a woman, but to my understanding this was just a stepping stone to move on to having the game played between machine and human.
I don't think the gender specifity was meant to stick around beyond that initial introductory example. If you mean how he says things like "imitation of the behaviour of a man", that's most likely intended generally rather than specifically male (particuarly as the "machine takes the part of A", which was the man pretending to be a woman).
