My brother has self-diagnosed himself with Asperger Syndrome (AS), and from what I've read, he's probably right.
I'm sorry to hear about your own diagnosis. My understanding is that AS is a fairly large collection of symptoms or tendencies and that not all AS people exhibit all of them. There's lots of info available on the web, as you've no doubt discovered. Just google "Asperger syndrome." Several dedicated websites.
My brother's key moment was when he came across a book by Temple Grandin, a high-functioning AS who has enjoyed quite a career designing the chutes that guide factory-farmed animals to their deaths in a human way, without evoking their fear reflex. He suddenly realized that he wasn't just "different"; that he actually had something, a syndrome, that had been described by other people.
My brother is exceptionally intelligent (an IQ of 190 when tested at age 6; mine was something like 160 and that made me the stupid one). He upset his Fourth Grade teacher when he sat in the back of the classroom reading my mother's old organic chem textbook, college level. He went to MIT at 16. Indifferent grades. Was very fond of building "devices": fuzz-boxes of every conceivable type; a whole recording studio at MIT, which he handwired from the bottom up. A recumbent tricycle.
He's described one key symptom of AS as an inability--often quite disconcerting to others--to decode the emotional subtexts of conversations. "An inability to process social cues." He was fired from many jobs for simply ignoring what his boss asked him to do and spending his time doing something else that he thought was more important as an R&D focus.
Here's AS, as exemplified by my brother: Somebody says to him, "My mother died yesterday." He says: "Did you know that after the human heart has stopped beating, the body cools at exactly the same differential rate as a refrigerator warms if you unplug it?" True enough! But wildly missing the point.
That's my brother.
A second key symptom, implicit in this first: things are more real to him than people. Those fuzz-boxes had feelings, as far as he was concerned.
Now, as the owner of a series of old cars, I understand this. God knows I feel for my cars. I can FEEL when the oil level has dropped and the cams start to complain. Since I shared a room with this guy for the first 12 years of my life, I've often felt that I had gotten a bit of "contact AS," if you will.
About running: my brother played his share of soccer back in school, and he still bicycles a lot. He wasn't particularly athletic or well coordinated.
Over the past decade he's put on more than a hundred pounds. So no: he's not doing much running.
I think, frankly, that running would be a great thing for an AS sufferer. (Is "sufferer" the PC term? Probably not. Sorry about that. Really!) AS people have incredible focus; they often accumulate amazing stores of knowledge about esoteric things--such as train schedules, a classic AS riff, or cars. So the many aspect of running physiology and training could become such a focus.
Running is a wonderful way to spend solitary time. You can get lost in your own head. Yet, especially if you're running outdoors, it's also a great way of keeping in touch with the "world out there," which is something that AS people need.
My worry about putting AS together with running would be that AS people, who can be prone to isolating themselves in their heads, might literally drive the car--their body--into the ground, failing to pay attention to the cues (somatic intelligence) that non AS people routinely attend to.
Then again, most runners know how to avoid paying attention to that stuff. They "just run," and run too hard some of the time, and do OK.
Good luck with your journey.