In short, he of the "tag" system, of which more later is either a parenthetical apposition, or a case of true, isolated parenthesis. In the former case, you could replace the brackets with commas; in the latter, dashes.
It is parenthetical in that it stands apart from the syntax of the rest of the sentence, just as with dashes (I love Rhodes—who wouldn't?—despite the weather.). However, in this case the brackets could be replaced with commas without rendering the sentence ungrammatical; that is, it would be a bit awkward, but still correct.
But this idea has been a driving force in mathematical logic and computer science since Alan Turing, A. N. Kolmogorov and Emil Post, he of the "tag" system, of which more later.
Here it would be an apposition to Emil Post. The simplest type of apposition looks like this:
Clytaemnestra murdered her husband, King Agamemnon.
Nero's cronies killed Agrippina, her/she who gave him life.
The reason why he (not him) is used in your sentence could be that Emil Post is the subject of the elliptical clause "since Emil Post presented his theories", or something like that; in that case, he is used to indicate that the apposition belongs to the subject.
As an alternative, one could say that the nominative he is used because this happens to be the typical case for appositions in modern writing. This goes against the rule that subjects and subject complements (and only those) should be in the nominative case in traditional style, but it wouldn't be a first. I'm not sure what to think of this position.
Lastly, it could be argued that it is not an apposition at all, but rather a case of truly isolated parenthesis, which could be rendered by dashes without change of meaning:
But this idea has been a driving force in mathematical logic and computer science since Alan Turing, A. N. Kolmogorov and Emil Post—he of the "tag" system, of which more later.
In that case, there is no syntactical connection at all between Emil Post and the he phrase, just a semantic/pragmatic one.
Of which more later is simply a relative clause that modifies the "tag" system: nothing complicated or controversial there.