I think the useful distinction is that, when you teach multiplication as a mechanical computation (arithmetic) it's useful to talk about it as repeated addition.

As you get to negative numbers, rational/irrational numbers, complex numbers, matrices, etc. it becomes more useful to think about multiplication in more abstract ways, among which repeated addition is still often a useful way to look at it.

I also think it's not particularly useful to talk about those other ways to think about multiplication until you actually need to.

It's too easy once you've mastered the concepts to forget how beginners look at them and struggle to understand them. I think the author isn't remembering what it's like to try to understand multiplication as a new concept - I certainly can't remember.