So, where was his rifle?
You can't hold a rifle and a camera at the same time. And the mountain lion is certainly not going to let you do a selfie with him. This has to be captured on camera. Priority.
“So, where was his rifle?”
That was my first thought. But maybe he thought he could keep the cat in his vision easier and could get quicker shots off if he had to. If he’s elk hunting, he probably has a bolt-action .338 Win Mag, or least a bolt-action .30-06.
Maybe he was Archery hunting with a bow and arrows...