If we were to dissect this construction utterly literally, would it be something like "what (is) the hour that it is?”
(Or in the original word order, "what the hour that is it?")
Yes. What is the hour that it (ie. the current moment) is or what is the time when/in-which it is.
Compare also the construct nuair a bha mi òg when I was young from older an uair a bha mi…, lit. the time/hour when I was…
As usual, thank you very much :-)