This is literally what Amex said to me:
So their categorisation does have a direct relationship to points earn. As you mention, the example you use is because supermarkets is restricted to the merchants listed by Amex, and obviously WISH gift cards is by Woolworths.
Sorry, it's not clear to me how categorisation as a hotel versus restaurant affects points earn? Wouldn't you earn the same points either way?
All I'm saying is, I don't think retailers can decide for themselves whether they qualify as a "major supermarket", where transactions earn 3 pts per $. And as I mentioned, not even all retailers owned by Woolies qualify, so it's pretty clear there is more to it. I'm guessing there is a list of specific merchant names that qualify for 3 pts per $, as opposed to a category.
Anyway, regardless of how mysterious the workings of this are, I just plan to make hay while the sun shines!