I think the DA clearly threw the Book at the officers.... listed every violation, no matter how small....
It ain't a term for nothing.
The drunk Mr Brooks being shot in the back while running away, was absolutely, uncalled for, they were not faced with a deadly threat....
And according to every legal article I read, what the DA did was a catastrophic mistake. He grossly overcharged the officers, almost guaranteeing that they are exonerated by a grand jury.
As per your second contention, Brooks established himself as a "deadly threat" the moment he fired the taser. His willingness to use a weapon against police demonstrated that. It demonstrates that Brooks would have used any means at his disposal to prevent the police from subduing him.
And as per the next contention:
He was running away, yes, while pointing his stolen taser at the officer. Notice his positioning in the video. He turned his right arm and upper torso toward the officer while maintaining a forward motion. His back remained exposed to the officer who ultimately fired the shots. There was no way he was simply fleeing. He had a weapon. He fired. He died. His mistake, not the officer's.