Hey Mar. Cool topic.
It looks like the child hasn't learned how to play with others. This will take some time and regular application of play-time to correct. Here it is awesome that you've already started playing games with her as this begins her process of learning how to listen, pay-attention, follow guidelines, and slowing herself as she interacts with others and something from her physical environment that requires to be understood. Continue being patient and breathing - she will eventually 'get it'.
When children play together, you will hear 'they don't want to play with me!' a lot - this is specifically the case when they just begin playing and cannot find common interests or if they've been playing for an extended amount of time. In the case where you've got a 'play date' with another child in your home, I would be prepared with activities that I could do with the children to give them an opportunity to get to know each other - you could try painting, coloring with crayons, watching a movie, or having a meal together. We're having some kids coming over to our house to play next week that haven't played with each other before so I purchased 'Shrinky Dinks' (Google it!) which are an inexpensive little craft that we can all do together.
When you hear, 'they don't want to play with me!' After they've been playing for awhile, suggest to the children to take a break and assist them to find something else to do together that they would enjoy.