Your last post rang minor alarm bells for me about girls with aspergers - it was the "more interested in setting up play than the actual playing", particularly in combination with wanting to play her games her way... I have a girl with Aspergers and she doesn't play "normally" and it has caused some problems.
On the other hand, my 2nd daughter is most definitely not on the spectrum but is deeply introverted and absolutely fits the pattern of many introverted kids mentioned above - she has quite good social skills if she can be bothered using them, she likes people, she'd like to have friends, but she's not remotely going to play with people or play games that don't interest her at all, she'd much rather go and play alone and enjoy her own world. She CAN play cooperatively, she can play lots of different ways, with lots of different kids, but she WON'T play with just anyone doing just anything for the sake of having company. She's clearly one for a few high quality friends or solitude...
