a roofed often open passage connecting two buildings (as a house and garage) or halves of a building --MW

I was thinking of the breezeway at my old school--lovely, really, in its own way. It was a long enclosed glass passage between the main building and the building that housed the gym and library. When I wondered whether of troy's outside passage might be called a 'breezeway,' I was just wondering--I didn't realize that the definition of breezeway was so obviously restricted.

It would help to see a photograph, of troy, of an outside passageway to understand exactly what yours is like.