Considering he was a Christian, a human and well...kind of a non-action guy...I think Dante would have thought of Sto vo kor as a kind of Pagan Hell, where some sort of godless, frightful heathens live in horrible chaos and hedonism.
I just imagine him showing up there and asking to see God and some Klingon warrior telling him that they slayed their gods. He'd have the shock of his life at such a thought and the only way he could rationalize those Klingons into his world view would be either as demons or some savage, pagan culture from *gasp* outside Christendom.
As to "poetic descriptions" of gagh....again he was a human, not a Trekkie and not written as a character in Berman era Trek (which gave all humans a mandatory love for Klingon culture for some, unfathomable reason)....
I think he would have thought of it as some sort of ghastly hell food (as really almost anybody would)
So assuming he would have still written the Divine Comedy, he likely would have added both Sto vo Kor and the actual Klingon Hell to his depiction of hell, maybe he would have placed Sto vo Kor in Limbo...
It would be possible that he might have thought the Klingons were the Nephilim, forever trapped in some sub-part of Limbo and falsely believing in their pride that they have slayed god.