Firstly, I think it was done really well (gun shot scene in "Space Bound" video). It looked real and was very graphic, which is awesome.
Obviously, it's ruined by the fact he says 'temple' and he shoots himself under his chin, as it's too blatant to ignore given how well-timed it is and how clear his voice is.
I was trying to think why they would do it and I think I know why...
I think it was a little homage to Fight Club. Maybe either the director or Em just thought of doing that as a little thing but, anybody who has seen Fight Club will know... at the end, Ed Norton shoots himself in the mouth (so not chin but close) but his head blows back slowly like that...
And then Brad Pitt aka Tyler Durden aka his alter-ego dies. And then Norton is back to normal as he's killed the voice in his head you could say. So perhaps this was alluring to that idea, as you see the 'duplicate Em' in the cafe experience the same thing.
Uses a silver gun too.
And then it rewinds and Em gets in the car, perhaps suggesting his evil voice has been killed and he doesn't kill her or himself because of it.