Scheiner's cousin is also the definition of a hunter, like his grandfather, and he has no problem with killing, but he isn't very good at shooting a rifle. I'd still consider him almost just as much of a hunter as his grandfather, even though he isn't entirely Schiener's definition of a hunter, because he has the most significant facet of being a hunter.
He also shouldn't be seen as too harsh, even though he is willing to kill animals and almost let it bleed out. He was also grown into hunting, and it's not like he knew that it was cruel to let the rabbit bleed to death, and after he knew it was, he didn't let it happen.
The only thing that I think changed with the two's relationship with the writer is that now the writer doesn't want to go hunting with them anymore.
After the trip, Scheiner probably looked at himself in a different way. Instead of seeing himself as someone who could be a hunter because he can shoot a rifle, he saw himself as just someone who can shoot a rifle.
While reading this essay, I knew from the way he thought of everything going on that he wouldn't want to be a hunter. It didn't disturb me, because I've also grown up around hunting, but it made me feel disturbed for Scheiner because he probably thought of the experience as disturbing.
I believe all of the graphic discriptions he wrote about the rabbits he shot were necessary because seeing the remenants of those rabbits and hearing the thuds of the rabbit's heads against the truck were what made him realize he didn't have the characteristics of being a hunter.