I agree with you, it's not how technical people are hired. But, I think it's entirely necessary in certain contexts, once we realise the software world is bigger than just Web.
Learning languages and libraries is easy. But new paradigms, domains, and entire new ways of thinking? It takes time to master.
So I'd be inclined to add disclaimers to the idea that "after 6 to 12 months nobody will ever notice".
This might be the true if you're moving from 1 web programming gig to another web programming gig, but the author himself acknowledges the vastness of software out there that underpins every aspect of industry.
So - if you're going to be working on enterprise middleware in investment banks, or embedded systems on airplane simulation kit, or APL, or missile guidance software - but all you've done is web... then tech stack does matter. Insofar as being familiar with the paradigms, standard patterns and unique industry norms.
The problem is that some middlemen (ie recruiters, HR or non-technical hiring managers) do not understand that, for instance, Java and C# are somewhat interchangeable, but C# and APL are not.
Fantastically written piece in all though, lots of great stuff in there that I wish I had either known (or stopped denying!) earlier in my career. But specifically on this point I think it's a dangerous idea to imply to undergrads that deep, hard-earned experience in both tech and domain can be overcome in such small time scales.