No I don't think they are getting it for the reasons you outline @BonfireLady
I've not finished watching the whole thing but I found where he started talking about the binary way of thinking, labelling and organising- this is a very common autistic trait that comes from an early "deficit" from want of a better word.
Put simply, it's harder for some autistic children to flexibly transfer details across categories. (The simplest level would be how much dogs vary and how to tell the difference between a dog and a cat. It can result in favouring certain things eg a particular restaurant and a particular item off the menu because it's predictable. Knowing that a Mac Donald's can look one way in one town but another way in a different town, with the same menu, may have to be explicitly taught.)
Skilled educators (speech and language specialists would be key here) need to be aware of this, and usually are in send settings designed for autistic learners.
But more academically able autistic students may not be in those settings and may develop frameworks to interpret the world without anyone realising, which with sex / gender stereotypes, can very easily lead to the binary thinking he describes.
Which is WHY it's SO important to be challenging gender stereotypes from a young age; neurotypical children also do this anyway, schemas, categories and frameworks develop naturally from very early on and rely on gentle adult support to develop in nuanced ways that aren't too binary. It has to be age appropriate too. But it can be harder for those with specific language difficulties and autism.
And then you've the internet confirming everything. I was once part of a synesthesia group on facebook and some were obsessed with gendering objects and numbers etc. it was clearly very gender stereotype driven.