I realize the author learned from the situation and I hope they're a better person now, but I would certainly consider their behavior abusive.

It's fortunate the kid was just dealing with dry skin. Imagine if it was something like OCD where they were dealing with an irresistible compulsion and had no way to express what they were experiencing. Is spanking an acceptable response? How about one or both parents telling them to just stop? Rubbing spices all over their hands so an already terrible experience becomes worse?

Perhaps I'm too invested in this because I grew up with an undiagnosed neurological disorder and was punished similarly. The punishment and derision from my parents took a serious mental toll on me that I'm still unpacking.