The setup you propose is interesting — I’ll consider it from two perspectives. Firstly, as a philosophical question, and secondly, in a realistic format (with the technology we have available today).
Philosophical: If the interrogator were an intelligent machine, this is a sort of all-powerful sword vs. invincible shield situation (one claims a sword can puncture any shield, yet simultaneously claims a shield can deflect any sword). Assuming both machines (the player and the interrogator) are equally intelligent, I would say the interrogator would have a 50% chance of guessing the right person. This is what Turing’s rebuttals converge to as well; when machines are developed to the point of equal intelligence as humans, the interrogator, human or machine, could only guess randomly. When the machine player is truly intelligent it could either try to replicate a basic human response as possible or try to be more human in a sense by using cultural references and deeper aspects of language. However, since a machine interrogator would think the same way as a machine player, if the machine player stuck to only one strategy (either being a ‘normal human’ or being ‘more human’) the machine interrogator could simply infer which player was the machine based on which one acted more ‘normal’ or ‘more human’. The same applies for the human — the human player, who is unaware of which strategy the machine picks, may choose one strategy or another in the hopes of convincing the machine that they are the human. In the end, the interrogator must choose between which strategy — normality or ‘boosted humanity’ — yields which categorizations. It is random. However, I am not sure Turing would think this way. Your scenario is a fascinating idea. I suppose the only way to find out is to wait until AI becomes truly intelligent and try it out!
Realistic: As someone who’s worked with AI, especially in Natural Language Processing (NLP, a field of machine learning that deals with text comprehension), I would say that a machine interrogator could tell human from machine player close to 100% of the time simply because currently, machines are much better at classifying text (such as dividing into Republican or Democrat, male or female, introvert or extrovert, etc.) than at generating unique text. The machine player’s text would be easily identified as plain, whereas the human’s text could involve more appropriate uses of more complex aspects of language like cultural references or metaphors. Even if the machine player wanted to, with today’s technology it would be easy, especially for a machine player, to identify which player was human and which one was a machine.
I hope this response provided some insight into a possible answer to your scenario!