Sounds inhumane to me, as well as illogical; no offense whatsoever intended to you nor the author, though I understand my thoughts on it may well be offensive.
If you pierce the brain itself, you've killed it; not merely paralyzed it. Anything less than brain death means you missed it or inflicted the most superficial injury possible, which is hardly humane.
To me this sounds like he's damaging a nerve, or nerve cluster, which is paralyzing the bird, then butchering it thinking its complete inability to express its agony proves that it's a humane death. Unfortunately I'd bet you they're suffering a gruesome and horrific death.
That's a very tiny and utterly necessary organ you're aiming for, you're going in through a very sensitive area to reach it, then somehow not killing it? Doesn't make sense.
It makes as much sense as the idea of stunning the chook before killing it. Have you ever been stunned with voltage or a blow to the head? In the majority of cases, all it does is stop you from crying out or moving, but it certainly does not prevent you feeling any other damages that are being inflicted on you, and it's not painless in itself. But since they can't express their pain, it's easy to think they're not suffering. It looks neater and that's its only virtue.
There pretty much isn't a more simple, sure, swift, and humane death than chopping off their heads or breaking their necks. You sever the spinal cord and that's that. The nervous system may chuck some spasms but they're dead, no doubt about it. It looks more gory though, and can be messier, and as with any method there can be a failure rate based on the human side of the equation. But it's a better bet than stabbing them in the roof of the mouth with a knife or immobilizing them with electricity.
It does beg the question... How does he know this doesn't kill them? How long did he leave them before he knew it wasn't fatal, or under what circumstances did he find that out?
Best wishes.