It's probably too late, but keep that screen protector! The small coverage is for the curved edges on the Note 4 and it could be useful when applying a protective case for the phone since the glass provides space.
The tempered glass is meant to be cut short for the Note 4 because of the phone's curved edges. If the screen protector were to fit the whole screen then you would start to see a halo form on the edges of the screen protector