That seems like the American approach, yeah.
Not sure what's wrong with being Italocentric here. But what do we call the period from Gutenberg to . . . whenever we move on to the next era?
Age of Italian Imitation? Or does that sound too much like Italy is doing the imitating?
To my mind, it starts a bit later than Gutenberg. Let's say, around 1480 or so.
Now, I think you can call it "Renaissance" until the mid of the following century or a bit later.
But in Italy we tend to split it into smaller units ("Umanesimo", "Rinascimento", "Manierismo" and so on) based essentially on trends of art history.
A point is that different places, even within Italy, knew this kind of process in different times. Manueline Portugal was contemporary to the climax of Italian Renaissance, but its architecture was fully and clearly Gothic. And my hometown, barely one hundred kilometres from Urbino, had a basically "medieval" figurative tradition in early 1500s when Urbino, Rome, Venice and other centres were Renaissance in full swing with Piero della Francesca, Raffaello, etc.
I am no art historian, but provincial cities in Italy (not mention northern Europe) are really striking in this. You can see mixes of late Gothic and Renaissance everywhere, and even very late.
Similar things happened in philosophy, though here things are more complicated.
Places like Poland started being influenced by Italian styles when that stuff was already in relative decline in Italy (in the main centres at least).