I really love this. An amazing way of creating an organic conversation with the user and will therefore, I believe, lead to a better user experience and conversion.
There’s just one thing: the user doesn’t know when the conversation will end. What will be the duration of the conversation? How many questions? What’s the progress of the conversation?
This is usually a very important UX part in forms. How would you integrate this in a conversation? Could you still indicate a visual marker? Although that would maybe take away the organic and natural flow of the visual interface of a conversation.