Hi Isaiah09,
The current diagnostic criteria for Asperger's Syndrome are here:
https://www.firstsigns.org/screening/DSM4.htm#AS I find Asperger's the most likely among the autism spectrum diagnoses to be considered by a neuropsych, because it sounds as though your DS didn't have significant language delays, and certainly not an IQ impairment. But there are links to diagnostic descriptions of all the various shades of ASDs from the top of that web page.
Good eye contact alone is not enough to rule out an autism spectrum disorder. They are looking for clusters of features that add up to a social disability: a failure to engage and relate to peers well, an inability to adequately understand the thoughts and feelings of others, impairments in social language, impairments in nonverbal communication, all these sorts of things can be part of the picture.
There is so much folklore about autism these days (i.e. "he can't have autism because he ... fill in the blank"), and a lot of it is not correct or not that useful for a family wondering how to proceed. Expert advice is much better.
Don't panic. See what the neuropsych says. Make sure they do a thorough range of testing. Ask them lots and lots of questions, and make sure you don't leave after the followup meeting until you understand exactly what THEY think you should do next (a new school that's a better fit, or special services, or whatever-- a clear path forward should be the goal.)
HTH,
DeeDee