Algebra based designs can be formed around many data structures and many languages generalize this concept like Haskell. With Haskell you can create your own algebraic DSL around arrays and anything else you can think of. It seems he's enamored with the specific array instance of algebra based designs and unaware of how it's only one specific case of a general concept.
An APL-like Haskell DSL could be interesting, but to match APL's expressiveness you'd basically need to reimplement all of APL. For maximum generality, one could just skip both APL and Haskell and just use the lambda calculus. I found that a bit hard to work with, though.
As far as Numpy and all, they are all directly descended from APL. The only difference is that it takes 10 lines of Python to match 15 characters of APL. While the array languages' terseness can be excessive, doing it in Python is not very pleasant either.
Anyway, here's somebody who knows more than I do talking about what they like about APL's successor, J: https://www.youtube.com/watch?v=RWYkx6-L04Q
I don't think you can attribute this to ignorance, because it's very clear that Pike is not ignorant of programming language design - even if you disagree with his decisions, he has had tremendous success at implementing his vision. To me it speaks more of disinterest - FP doesn't seem to really register on his radar as a useful mine of PL ideas. That's fine, although I agree with the previous poster that it's ironic to be such a proponent if APL, and yet have such a blind spot to another very fascinating area of his field.
I remember having a course about programming paradigms which introduced different languages and we wrote a small project based on functional languages.