I find this encouraging: the school has a level of awareness, and Asperger's is not a deal-breaker. While your DD's level of awareness is also encouraging, it could be that the difference she notices is mostly being out-of-sync with peers due to giftedness.
When DD spoke about her play to your friend, did your friend affirm your DD's interest and reply to what your child was saying, providing a smooth segue to the new topic your friend introduced... or did the friend change the topic abruptly, seeming not to respond to your daughter's shared thoughts? Role-modeling the desired conversational style may be an important reinforcement for learning social skills.
