Oh, sure! Occasionally. In moderation and with care. Not, in other words, the way they're used in the linked farrago.
Personally, I think I'm OK with this use, as it's supposed to be a kind of list after the colon. Isn't the proper use of semicolons somewhat subjective, anyways?
Abusing semicolons in this way is, in the most strictly pedantic sense, not syntactically incorrect inasmuch as a semicolon joins independent clauses. But that's like saying you can use a flathead screwdriver in place of a cold chisel. Sure, if you hammer on it hard enough for long enough, you can eventually muddle through, as long as you don't mind making an unserviceable mess of the work. But it's still the wrong tool - just as are thirty-five semicolons here.
Syntactically permissible or not, this usage is nonetheless an error, not because it is stylistically grotesque - although it is also that - but because it actively impairs legibility rather than promoting it.
It’s way worse to write like you do than to list stuff out with semicolons,