Did Roman society have a word for what we today associate with being on the autism spectrum? How was it treated?

The short answer to your first question is no, Latin has a much more limited vocabulary when it comes to medical issues and a much less robust understanding of those issues.

However, just because you don't have words for it doesn't mean it doesn't exist. To quote from an old response I wrote to a similar question:

Autism is harder to pinpoint since the term refers to a range of issues caused by different factors. Since it isn't immediately obvious at birth, it isn't likely that autistic children were exposed for their disability. However, ancients lived much closer to starvation and had much less free time than we do. A severely disabled child was probably not likely to survive and even if parents wanted to help, it's unlikely that they would have had the resources to do so. If it was a mild form of autism, then they're likely to have been able to function and probably wouldn't have even attracted much interest.

There isn't a ton written on the subject. The Blackwell companion to Science, Technology, and Medicine in Ancient Greece and Rome discusses it briefly and demonstrates the issues of evidence. Gershon Berkson at UIC has published a couple of articles in the journal Mental Retardation (I can't believe that's a real journal name) about mental disability in the ancient world, particularly Down Syndrome. Obviously not a historical journal, but it still seems to be a solid argument.

One interesting note: way more people in the ancient world were involved with agricultural labor than people today (thank god for mills and farm machinery!). Some scholars who work on this questions have argued that the repetitive nature of farm work and labor in the ancient world would have made the environment of the ancient world far easier on autistic individuals than the varied tasks and environments we ask people to deal with today.