There no mention that the pope is a King. Those are your words.
Sorry. Sister Bernadette taught me to translate as literally as possible.
[Latin : inter-, inter- + regnum, reign; see reign.]
A king reigns, a vicar does not. And I understand that one of the secondary definitions is a period between governments.
My original question remains: Is this a term a that is normally used when we are without a pope?
It just seems imprecise. Maybe we don't have a better term.
I guess I should have Googled the question when it first came to me. It appears interregnum is the term normally in use.
And, as the pope is the temporal ruler of Vatican City, now it makes more sense to me. Yay!