The Romans in the 1400s still called themselves Romans and saw themselves as Romans (in Greek: Rhomaioi). They never stopped.

So, no, it's not at all like calling the Iraq war a British Empire endeavour.

It was our own much later civilisation that made the historical distinction between the older East and West combined "Roman Empire" and its continuation in the East (and sometimes in the West) post ~476 AD ("Byzantine Empire"). The Romans themselves never saw the distinction.

in a sense it is.