In this particular case, Hughes’ arrows are a practical implementation of a Profunctor Categorical Structure. They are roughly a generalization of what arrows (as in function types or more accurately relations) are.

In the article, author is pointing out that the selective applicative doesn’t seem to work correctly (in a categorical sense) for functions, but when generalizing to profunctors a near semi-ring structure appears and works for the SApplicative.

I am pretty sure I’m reading TFA correctly here, but I’ll check when off mobile and edit if I still can.