I agree. מבנה can mean any kind of structure, whether it's a building, a bridge or a monument. That's why I think the translation here isn't great; from the way it sounds to me, if he says "מבנה" instead of "בנין", it's probably to indicate that it does not fall into the category of a בנין.
“I live in this structure” was accepted for me. In Hebrew, הזה means either this or that. Even in English, if someone were to point out an abandoned hut that we were standing right in front of and said אני גר במבנה הזה, either this structure or that structure is okay and natural as a translation.