Neil de Grasse Tyson’s academic output is exactly what you would expect from someone did a phd then left research science. He has a few first author papers that have a couple dozen citations and a few papers where he’s only a contributor. He hasn’t written academically since then. He’s not doing active research, which may mean he’s fallen behind on the cutting edge, but that doesn’t mean he’s not qualified to talk about astronomy with the public. He has the relevant training and knowledge.
Emil Kirkegaard, whose blog you linked to, is not a reliable or unbiased source for this kind of judgement for a wide variety of reasons.
The gist of this article seems to be that Tyson is "not much of an astrophysicist" because he has too many social media followers compared to the number of papers he has published.
He sounds like a bureaucrat that just climbed the hierarchical ladder.