My wife of thirty years is a special education teacher. I also do optometry in a number of facilities with a few of them including the population you mention. I also have run a chess club for the last 3 years where one of our very regular members is a young man with Asperger’s Syndrome. So I have knowledge and experience in working with those in this population you mention.
The young man with Asperger’s, in my club, is about to leave the area to go to a university 60 miles away. He spent the last 3 years at the local junior college, living with his family. I have talked numerous times with his mother and father regarding working with him and helping him do well in life and chess.
This guy’s manifestation is one that is very often seen with Asperger’s, he won’t look you in the eyes and his communications are less than social. He doesn’t use profanities as in other problems, but he is certainly the opposite of being social and outgoing. Actually Chess is a great activity for him.
After being in my club and my working with him for about 7 months, his mother came to see me saying how much he enjoyed and looked forward to our club meetings. I think he has only missed a total of 5 meetings in 3 years. He also extroverted quite a bit after being in the club, and he would surprisingly start talking with me and then others on various subjects.
For the longest time, he was only second to me in Chess playing ability in the club. Only one of the 3 new player adults have surpassed him at this time.
Getting him to study anything like openings or tactics is nigh impossible. So, he doesn’t know openings or even use the same opening moves in any regular fashion. I found that setting up tactical positions on the board and having him, along with the others in the club, provide the answers was interesting yet productive. He would snap out his answers and when I would say it was wrong, he would question me as to my accuracy. I would then explain the answer and the proof of why his move(s) were wrong with the pieces, “OK, if you make that move, White would make this move and you would not win as you could.” He did make progress in time.
It has been offered that Bobby Fisher might have had a mild form of Asperger’s. I don’t know.
Now, in the case of those with lower intelligence, I have found starting with less pieces on the board works best. I have had times where we play the pawn game (only pawns on the board and the first one to have his pawn reach his 8th rank, or the opponent cannot move and the player can, wins) for many weeks before introducing any other pieces. I also have worked with endgame ideas, like Q & K vs. K.
There also was a game made with far less squares and pieces than the regular chess set for learning. This might work.