A real conversation is about conveying understanding, not about the words spoken.
AlphaGo was trained on however many zillions of games and playing against itself, but does it actually understand anything about the game? Or can it simply react to the current state of the game and suggest what the next move should be. It will never have a leap of intuition causing it to say "the only winning move is not to play."
Intelligence is not purely reactive.
Basically, you need to ask questions that require meta-cognition, like, "What does Mary think about you?" That requires:
* Understanding of yourself as an entity.
* Understanding of Mary as another entity, with its own state.
* The capability to use previous interactions to approximate that other entity state.