[nostrademons]

The article is making a very important point:

Even for things as "objective" as mathematics, definitions ultimately come down to what makes it convenient to manipulate symbols like an expert would.

This comes up all the time in fields as diverse as software engineering, law, finance, business, even hard sciences like physics - things are "right" because they're convenient, and because the consequences of them being that way make it possible to build on those results with new constructs, while doing it a different, more intuitive way would result in those constructs being impossible.

What the article is saying is that your intuition for it being 0 or undefined is because you've been exposed only to exponentiation as repeated multiplication or as the limit of some series; if you consider other theorems like the binomial theorem, and figure out what is necessary for them to hold without special casing, you'll decide otherwise.