Doctor Kind found himself in 1986, before all the changes, before the machine had even started working. He knew where to go, where to look. It was the Reagan years, so buying a gun was easy.
The grad student Kind used to like to go to this particular coffee house; Emily worked there then. This was before he had gotten up the nerve to ask her out. That’s where he found the his younger self, and that’s where he now pulled out the gun and shot him in the head.
This way, the timeline was safe, and Emily was protected.