This particular essay and position occupies a rather interesting point in Buddhist history. Nyanaponika was responding to the then-popular idea endorsed by CAF Rhys-Davids (among others) that Nibbana was the True Self and hence that Buddhism was no different than Hinduism.)
While that argument would find few supporters among contemporary serious students, it is also the case that Nyanaponika’s response (shared with other Theravadins of the time) is not quite right, either.
As point out long ago by Ven Kheminda, the teaching that “all things are not-self” is said to lead to dispassion, revulsion, and so on, and so can hardly be referring to Nibbana. In fact it is a guideline for vipassana meditation.
The reason for the difference between the use of sankhara and dhamma is not because one of them includes Nibbana. It is because dhamma here means “principle” as in, the laws of nature: dependent origination, the four noble truths, and so on. They are descriptions of how the world is, so they are not themselves “impermanent” (since they are always accurate descriptions of samsara) nor are they suffering. They are, however, clearly not self.