Actually, I think that chess is the type of activity that could be easily mastered by people on autism spectrum, due to its rational nature. I used to be in top 50 players of my age category nationally and I must say, that several people there clearly showed signs that they might be on the spectrum. Also, best player of my country is probably an Aspie (shy, weird type, who is distinguishable from distance by his awful clothes and clumsy moves; also I heard some stories from his former coach and it appeared that even as a kid, he was interested in chess to the point of obsession - always carrying some chess book with him, memorizing the entire games, etc.).
Personally, I am not really good player, especially because I have never got anyone to train me, and I really suck in learning the opening theory (several players commented that for my playing strenght I have unusually low knowledge of theory); that contributed to my playing style: I am strategic player who tries to survive openings, create complicated, but closed position with multiple weak points in positions of both players and then slowly overpower the opponent. Because of that, I am much better in longer games than in blitzchess.
What is interesting is that I am good at blindfolded chess; I can keep up there with players who are normally fairly beyond my playing strenght. I would attribute that to the fact, that I am good in visualizing. I have also no problem to play more than one blindfolded games simultaneously; my personal record at blindfolded chess was three games simultaneously combined with the fact that this was played in a bar; it was very noisy place, I could not concentrate very well, but it did not prevent me from winning all three games. 