Also, the lyrics of the song are VERY important to the characters. Watch the scene again and notice:
A. It starts as soon as Carmela walks in
B. The cuts match the lyrics - "small town girl" = Carmela; "city boy" = Tony; later on: "some are born to sing the blues" = Tony; the list is nearly endless.
Of course, its abrupt cut is instrumental to what the final episode stands for.