Well now, did the big kid use a little disproportionate force? sure, the little kid could have been seriously injured.
However anything less might not have convinced the little punk to cease and desist.
It's not realistic to expect anyone, let alone a child, in the heat of the moment, to determine and employ the exact amount of force, but no more than necessary to stop an attack.
It's what happens, not what could have happened that matters.
It would have been a tragedy if the little kid had been paralyzed, or something, but a few bruises, even a fracture?
Children are often exonerated for intentionally and without provocation causing injury, so this kid sure as hell shouldn't be facing any punishment.
A sharp blow from the heel of the hand to the base of the nose results in instant death (since the bone is driven into the brain).
This is actually a myth, the nose is mostly cartilage without the tensile strength to drive it into the brain, Even if the nose was completely made of bone it wouldn't be long enough to reach the brain and you would actually have to drive bone through bone as there is virtually no chance of any bone fragments finding their way through the very small openings in the sinus area of the skull.
Such a blow could indeed be fatal as any hard blow to any part of the head could cause brain trauma, but there will never be any nose bone missiles ripping into anyones brain.