The Greek word for "ruler" or "prince" in these passages is archón. And in his translation of the New Testament Hart transliterates the word, giving us translations like "the Archon of the demons" or "the Archon of this cosmos." You see this in other familiar passages as well, like Ephesians 6.12:
Because we are wrestling not against blood and flesh, but against the Archons, against the Powers, against the Cosmic Rulers of this darkness, against the spiritual forces of wickedness in the celestial places.
Just who or what were these Archons, Powers and Cosmic Rulers? Hart comments in his footnotes on some of these texts:
[T]he reference is not to earthly rulers but to celestial spirits or angelic beings governing the nations, in whom most of the peoples of late antiquity believed in one form or another, and who were quite prominent in Jewish apocalyptic tradition (influenced by Persian thought)...[These texts are] full of associations with the complicated angelology and demonology of late antique Judaism and Christianity, dependent to a large degree on such intertestamental texts as 1 Enoch and the book of Jubilees. One should not assume, incidentally, that these superterrestrial powers were understood simply as fallen beings; elsewhere in Paul's thought (Galatians 3:19 in particular) there seems to be a mention of angels who function as deputies of God, yet perhaps do so ineptly or recalcitrantly; and there is even a suggestion (not necessarily intended as irony) that an angel might deliver a false gospel (Galatians 1:8). Moreover, central to Paul's eschatology is the certainty that in the Age to come creation will be freed from subjection to all celestial powers and ruled solely by Christ and, through Christ, the Father (see, especially, 1 Corinthians 15:24-28).
As Hart elsewhere notes about the origins of these Archons:
For Paul, these "powers on high," "archons," and so on are are the gods worshiped by the several nations, but are ultimately only angelic governors of the cosmos, often either rebellious or incompetent; this seems to include even the angel governing Israel, who, according to Galatians, delivered a defective version of the Law to Moses. In Paul's time, the idea of angelic "gods of the nations" would have been, for instance, an unproblematic interpretation of Deuteronomy 32:8-9, which describes God as dividing the nations among the "sons of God"...[It] is a large part of Paul's understanding of the gospel that these cosmic "gods" have been conquered and placed under proper order by Christ and will, at the end of time, be handed over in proper subordination to the Father so that God may be "all in all."
If you're a regular and long time reader of this blog, all of this will be very familiar to you, as I've written a lot about "the principalities and powers," the angels of the nations, and Christus Victor visions of salvation. All that to say, Hart's translation has the virtue of bringing all this cosmic strangeness into view.