The child doesn't speak (yet), so he wouldn't get diagnosed with Asperger's. The term is also outdated by now, neither DSM-5 nor ICD-11 uses it. According to the DMS-5, he'd likely be placed on level 2 or level 3 autism, not level 1 (mostly similar to what was called Asperger's), depending on his daily life skills.
I suspect someone mostly non-verbal at his age (12, or thereabouts) would definitely be diagnosed with level 3 ASD, however it's hard to know what else he has issues with aside from communication - he's in a completely different kind of environment to modern kids, with servants and so forth who'd be dealing with may of the day to day things that a modern kid would be expected to be handling on their own by that age (and which would normally be considered in an assessment).
because in the late 2000s it became "the diagnosis of choice" for "Being an asshole in your primary social group" primarily aimed at teenagers.
Hardly - the push to merge Aspergers into the broader ASD diagnosis was driven largely by the recognition that there were fewer differences between Aspergers and "classic" autism than there were similarities, so having a separate classification for (effectively speaking) "autism with only limited verbal communication impairment" wasn't a good approach.
That said, the fact that there
was that "special" version of autism, particularly one which was fairly easily recognisable in successful people working in tech, at a time when tech industries suddenly became very visible, may well have contributed to that reasoning - having separate diagnoses, one of which could be associated with successful people while the other had strong negative associations, was just reinforcing the stereotypes and challenges. "Oh, you've got Aspergers? I guess you'll drop out of college and get rich then!" - not particularly helpful if you have sensory sensitivities that make you unable to handle working in an office, or any of the other "impairments" that would have to be assessed as having a significant impact on your life in order to actually
get that Aspergers diagnosis. "Oh, you have Aspergers" was far too often treated as code for "Oh, you're a bit weird but you don't
really have any excuse for not being able to fit in and succeed in life". And at the same time, it meant that autistic people who
did have communication challenges, particularly when they were young kids, were hived off into the "classic" autism diagnosis where they were treated as less than human, regardless of what their actual capabilities and potential were.
Merging everything under the Autism Spectrum Disorder umbrella was definitely a step forward, both diagnostically and for the actual autistic people involved. It's still far from perfect - the levels are based on support needs, which is a nice enough sounding idea, but it doesn't exactly capture the constantly changing challenges and coping capacity that autistic people live with, particularly for those assessed at level 1 (roughly analogous to Aspergers, though not quite). But it does at least shift the focus away from what's wrong with autistic people to the support they need . . . kind of, nominally. We're still progressing down that path, and the diagnostic criteria haven't really followed yet - they'll get there eventually . . . probably.
Not going to go into the links Hans Asperger had with the Nazis and their euthenasia programs - that's a whole other kettle of fish. Not least because Asperger's publications came out much later than work by Grunya Sukhareva in the Soviet Union, work which was arguably much better than what Asperger produced, and might have made the world a much better place for autistics if it had gotten wider recognition . . .