The gorilla’s initial reaction the boy falling into the moat was gentle; you could say very gentle considering his immense size and strength. Harambe appears to hold the boy’s hand or arm and lift him up. Understandably, the boy screams probably not because of pain but because the fearful sight before him. It could be said that Harambe was guarding the boy during a difficult moment much like a father protects his son.
Harambe does then rather violently drag the boy through the water as he moves fast but this is probably the insensitive behavior, by our standards, of a silverback gorilla. For Harambe his behavior is probably non-threatening and relatively gentle. Perhaps he was taking the boy to a safer place, a quieter place as there is considerable noise from spectators.
Cincinnati Zoo Director Thane Maynard confirms that the boy was not under direct threat or attack. It was just the possibility of Harambe harming the boy accidentally due to the silverback’s great strength.

I wonder, like many others, if the zoo made the correct decision to kill Harambe. Personally it was the wrong decision but I understand the difficulty. Harambe was an innocent player in this tragedy. Humans created the situation under which he was shot dead. A vigil is being held outside the zoo for Harambe.
In a previous post I said the zoo was negligent in a legal sense. I stand by that.
I completely agree with you Geri. Also as you say the people screaming made things worse. He dragged the boy away. It looks rough but not by the gorilla’s standards. The boy was concussed and scratched but nothing serious. People made this go wrong. People created the conditions under which this animal, who is very close to us genetically, was shot for doing nothing wrong. The zoo are going to improve the barrier. Too late.