No, in other languages you would write one function that specifies how to perform an operation per type, then reuse that, and most linear algebra/numerical libraries come with these defined for you. In languages without polymorphism, such as C, you might have special names for these functions instead, such as vector_add. The actual use of these would look like '(x + y)' in Haskell, Rust, C++, etc. and 'vector_add(x, y)' in C, and would (or at least could) be expressions.
> . Which, by the way, includes idiomatic C++, Haskell, and Rust, in all of which overloading (+) to do something so specific would at best be seen in a purpose-specific library (like numpy) only, but isn't automatically present in the language.
Linear Algebra types/functions aren't automatically present in most languages. A library can be implemented to use this syntax to add vectors/matrices/whatever very easily, and many are [1][2]. Even if the library doesn't use '+' as the operator for eg. vector addition, it could, and it chooses to not use '+', but that is not very important.
> In most languages that most programmers use, for loops are common, and if all of those are replaced by expressions, you get a more expressive language (for dealing with arrays).
I'm not sure what you mean by 'more expressive'? Maybe you prefer a more declarative/functional programming style but for loops have their place in imperative languages. J doesn't actually force you to write all of you code in that style - the language has constructs that can be used to construct loops that look like imperative C [3].
> That's the point that the article is making, and you haven't addressed it at all.
The features described in this article are equivalent to a library implemented on top of Haskell, Rust, C++. The usage of such a library would even look almost exactly the same.
[1] http://arma.sourceforge.net/docs.html#part_classes [2] http://hackage.haskell.org/package/linear [3] https://www.jsoftware.com/docs/help701/dictionary/ctrl.htm