Turing did not leave behind many examples of conversations he thought his AI machine should have. One that appears in the 1950 paper Computing Machiner and Intelligence seems to indicate that he thought such a machine could compose poetry, do math and play chess:
Q: Please write me a sonnet on the subject of the Forth Bridge.
A: Count me out on this one. I never could write poetry.
Q: Add 34957 to 70764
A: (Pause about 30 seconds and then give as answer) 105621.
Q: Do you play chess?
Q: I have K at my K1, and no other pieces. You have only K at K6 and R at R1. It is your move. What do you play?
A: (After a pause of 15 seconds) R-R8 mate.
Careful analysis of the dialogue suggests however that he might have had in mind the kind of deception that is possible with AIML. In the first instance ALICE can have a category with the pattern "WRITE ME A SONNET *" and the default response "Count me out on this one. I could never write poetry." The "Please" would be reduced by the already existing "PLEASE *" category.
In the second case the robot actually gives the wrong answer. The correct response would be 105721. Why would Turing, a mathematician, believe the robot should give an erroneous response, if not to make it more believably "human". This reply is however analagous to the kind of mistaken replies ALICE gives to mathematical questions.
In the third instance, the chess question is an example of an endgame problem. Endgames are not like general chess problems, because they can usually be solved by table-lookup or case-based reasoning, rather than deep search. Moreover, there is a distribution of chess endgame problems that the interrogator is likely to ask. Certainly it is possible to interface ALICE to any type of chess playing program, just as it could be interfaced to a calculator.
Although many people think Turing had in mind a general-purpose learning machine when he described the imitation game, it seems at least plausible that he had in mind something more like AIML. Chess endgames and natural language can both be "played" with case-based reasoning.