It's especially sad to see this from an IEEE publication (even spectrum).
First, the major unifying concept in Maxwell's equation was the displacement current, a quantity for the changing field in a dielectric with units as current density. This answers the age-old question, "how do you have a current circuit when one part (a capacitor) is clearly 'broken' and not conducting?" Maxwell was the first to answer the question with a solid theory. So a better way to write the sentence you quote would be, "Maxwell’s equations explain how high-frequency flows of electrons in conductors generate electromagnetic waves, and they were also the very first to explain how an insulating material, where there is no flow of electrons, would also act in a circuit" Basic electromagnetics education fail.
Second and more to the topic: if we pretend that there is some sort of "magneto current carrier" (a magneton), then we can extend Maxwell's equations to cover a hypothetical magneto current. Pretty much any electric current-flow problem can be re-stated as a dual magneto current-flow problem. There are a lot of practical upshots to this -- such as making simulations that converge to answer much more quickly -- but the one most related to antennas is that you can demonstrate that the radiation of an antenna is related to the conduction gap between it's elements. For example, if you have a dipole antenna with elements separated by width d, then you can also model that as a "cigar band" (open cylindrical sheet) of magneto current. For a molopole, you might use a "washer" (flat cylindrical ring) of magneto current between the conducting element and the ground plane. This is not new. It's been used for decades. This is the shortcut to the concept that's been known for decades. You do not need recourse to any concepts in quantum mechanics.