Cryptography is not web tech.

This website is being served to you using cryptography right now (tls).

I took web tech to mean the technology used to serve the web - the differences with cryptocurrencies are manifold, the principal one being that billions of people use the web every day to perform important functions, compared to cryptocurrencies where most users are simply speculating on prices.

I think GP's point is this:

1) You cannot have cryptocurrency without the web, so it is web tech.

2) Computational cryptography long predates the web. It would be more accurate to say "the web is cryptography tech", if anything.

1) A depending on B does not mean A is part of B (though I'd dispute cryptocurrencies requires the web to function at all, perhaps you're thinking of the internet?).

2) Cryptographic libraries (many relatively recent, e.g. go or rust libraries) are definitely an important part of the web, they're integral to web tech if you define web tech as the tech that powers the web.