I believe the point they are making is that they believe the original author still does not "get it". I'm inclined to agree.
Recognizing that when people say one lacks empathy and rejecting what one believes they might mean by that and instead reinterpreting empathy to mean something they want it to mean is fundamentally a demonstration of a lack of empathy in what was likely the original context. Even if new interpretation technically aligns with the dictionary definition.
I want to be clear that recommendations that the post make are helpful and seeing the world as best one can from some others point of view is worthwhile.
At a fundamental level though saying I see your definition of empathy and reject it for my definition which I'll be happy to try to live by, while noble, likely is directly contrary to both parity's use of the term.