Earlier quoted context omitted.
"APL, and its successor J [...] provide a notational interface to an interesting model of computation: loop-free, recursion-free array processing." How is APL loop-free, exactly? Later they say: "Under this implicit lifting, the iteration space is the argument frame rather than a sequence of loop indices." So if I understand correctly, we have iteration, but no loop. But that doesn't seem like a really important dist…
I think "loop-free" just means the language encourages you to think without loops, even if the implementation may or may not use traditional loops under the hood. This is basically common to all languages with a strong emphasis on functional programming. Instead of looping, you perform operations directly on the arrays/matrices, and in fact APL and J are focused on matrix manipulation.
Also modern Fortran falls into this category. (I mention it because it's far from a functional language.)