I believe that is exactly what happened. He turned around and started to rush the cop, forcing the cop to empty his gun on him. The cop has no obligation to let the giant get to him before shooting any more than a person is obligated to let a lion get to him before shooting. Once you sense you are going to be attacked by something capable of killing you easily once it gets to you, you start you assault as soon as possible to end the threat before they reach you.
First reports were that the officer yelled "I'm gonna kill you."
Something I have said myself, but only for a reason.
What would make the officer say something like that ?
Especially since he appears to be the type who would not just say that casually.
If someone hit me so hard that my brain was spinning round in my head, I know what the next words out of my mouth would be.
I might not kill them, but I would certainly make sure they were at least unconscious.