You're literally putting words in the OP's mouth. Where does it say that it's "under threat of some sort of punishment"? You're making that up entirely yourself.
If it is done TO PUNISH the child, that's a different story, (and although you're insinuating to the contrary you have no proof of that at all, hence my comment about not knowing the full story), however nothing about the OP suggests that this is the case, but rather that it's the mother's concern for the health of her family, on which basis I stick to my assertation that it is not abuse.
Your ridiculous notion that "the reasons behind the abuse are immaterial as to whether it's abuse or not" is utter nonsense.
Sticking a needle in someone to make them cry is abuse. Sticking a needle in someone to prevent them from catching a disease is not abuse.
Stabbing a pen into someone's throat to harm them is abuse. Stabbing a pen into someone's throat to help them breathe is not abuse.
Spanking your wife because you're a kinky couple is not abuse. Spanking your wife because you came home drunk and felt like beating her up, is abuse.
If it's abuse to make someone wear a mask, then Boris Johnson abused the entire country. Nurses and doctors must be being abused all the time at work!