This article does not demonstrate understanding of the semicolon; it is used incorrectly in the first sentence, for crying out loud.
It uses the semi-colon to join independent clauses instead of a conjunction, which is fine. It might otherwise have read, “The semicolon is a profound public mystery, and the only punctuation mark that…”. Nevertheless, it isn’t a great showcase for the semi-colon’s usefulness. The writer could have invented a more elegant example to begin the article; the one they chose is a prime example of a semi-colon that adds li…
> the only punctuation mark that regularly unites readers and writers in deep-seated repugnance
There is not a subject and a verb; this is a fragment and does not stand alone. Prepending "it is" to the second clause would make this a proper sentence by making the second clause an independent clause instead of merely a noun modified by an adjectival prepositional phrase.
Edit: I nerdsniped myself and it might not be strictly accurate to call it a prepositional phrase; 'that' is technically a conjunction in this case used to link its own subordinate clause, but that subordinate clause still does not complete the clause fragment whose subject is "[punctuation] mark." It's still just a modified noun.