NY did away with the term "accident" long ago and uses "incident" now, as most of these are avoidable, especially by following the basic rules of firearm safety. There is no debate that this was an unfortunate event.
I have a hard time believing the "gun accidentally discharged", but rather that the trigger was engaged on a loaded gun with the safety in the off position.
My guess is it was leaning behind the rear tire and slid toward the bump/tailgate contacting one or both. The brothers were inline with the side of the truck at the rear with the younger brother facing his older brother to hoist the deer. When the gun slid it would have contacted the bumper or tailgate at an upward angle going through the boys back and hitting his brothers shoulder. Very sad