I agree punctuated evolution is a political term, which set off a warning when I read the article. It has always seemed to me punk-eek was more of a description of what we see in the fossil record than a theory of how the change happened.
Punctuated equilibria has one virtue, which is that it is derived from the fossil record, unlike the conventional Darwinian approach, which is to claim that the intermediate forms — the ones which “should” be found at what are clearly stark paleontological boundaries — either didn’t get fossilized for reasons not understood, or were once there but, everywhere they were once found, were eroded away for reasons not understood.