I'm OP but must have cleared my cookies and have lost access to that account.
It turns out that "Hyppolitus" does not refer to the mythical figure but to a real person, Ippolito II d'Este! The latter does not show up in a google search for Hyppolitus which led to my confusion.
I found the answer to this question after tracking down the source material (in translation). See p. 218 in Ancient Music Adapted to Modern Practice (ed. Claude Palisca, Yale Uniersity Press, 1996)
These three Latin verses were written in honor of my lord and patron, the Most Illustrious and Very Reverend Cardinal Ippolito II d'Este.
A footnote on the text says:
The anonymous Latin encomium has three lines of seventeen, fifteen, and seventeen
syllables: "Musica prisca caput tenebris modo sustulit altis, / Dulcibus ut numeris priscis
certantia factis, / Facta tua, Hyppolite, excelsum super aethera mittat" (Ancient music of late
has raised her head out of the darkness, / So that, with antique and sweet numbers, to compete
with ancient deeds, /Your great deeds, Hyppolitus, she might send high above the heavens)
Insofar as the interpretation, I think the word order is a bit misleading. A clearer translation might be
Ancient music has raised her head out of the darkness / so that with sweet ancient (musical?) numbers she might send your great deeds, Ippolito / above the heavens to compete with ancient deeds.
Being part of the revival of ancient greek music in the renaissance, Vicentino wants to honour his patron by immortalising his deeds in the same way that the mythic deeds of the ancient greeks were glorified, and with (he thought) the same music.