I think you hit these sorts of problems regardless though. You could say empire, civilization, polity, society, culture... They're all fuzzy classifications.
They aren't discreet terms. A civilization doesn't begin or end at a certain date.. unless you agree to some specific formulation. But, that will not be an exact fit when you try to apply it elsewhere.
Taken totally literally, civilization just means urbanism. But obviously, that's not what we're talking about here.
The 'fuzziness' is just a consequence of your (and the article's, and some comments, but by no means everybody's) idiosyncratic usage: by treating 'Byzantine empire' and 'Byzantine civilization' as if they were interchangeable terms, then you have to explain that civilization on the Bosporus did not end with the fall of Constantinople, as you did a couple of posts ago. If, however, you stick with the usage that is preferred by a ratio of 50:1, then the fuzziness and potential confusion goes away, as then you would be using two distinct terms for two distinct concepts.
Your last paragraph is a non-sequitur, as the issue is not whether 'civilization' just means urbanism here, but whether it means the same thing as 'empire'.
I assume the author of the second chart that you mention is doing the same thing.
Frequency of use is not the most important issue, but Google estimates 75,400 hits for "Byzantine civilization" (plus 15,400 for "Byzantine civilisation"), and 4.3 million for "Byzantine empire".