A cathedral is the cathedral it is to a person in the 12th century because of how that person views God, heaven and earth, human sin, etc. The cathedral simply isn't the same object to, say, an atheist brought up as a Buddhist in 20th-century Burma. The way subjects and objects relate is far more contingent for Heidegger than for Husserl. When you examine human beings as they actually exist in the world, you are able to find out what kind of creatures they are, what makes them what they are. In short, Heidegger came to believe that Husserl's phenomenological method was abstracting away all the juicy stuff that makes up the world we actually perceive. The world is something we live in. And living in it, thought Heidegger, is as essential a part of our understanding as the formal properties of perception. So, he thought he could do a kind of phenomenology of living in the world.
And here is where the dangerous stuff creeps in. Once you've established that human beings understand the world in different ways depending on all kinds of circumstances, you have also opened up the possibility that there are better and worse ways to relate to the world.
Morgan Meis seems to be arguing that when Heidegger said "Dasein" he meant "Germans". I've always been most impressed with the concept of Dasein because it goes the other direction entirely, refusing to categorize exactly who or what necessarily is Dasein. It got away from the usual "rational animal" crap, avoided the fundamental ethical preening about "what makes humans special", and just separated the quality of note from humanity.
It could be a cat. It might not be a human. It's definitely me, but that's all I can say.
Despite Heidegger's assertion of Germans and ancient Greeks being privileged by language and so on, the core differences from Aristotle understanding of being - what's millenially interesting about Heidegger (e.g. ontological difference, Ereignis) - work the same for all daseins, whether they are in indigenous tribes somewhere and haven't be stumbled upon yet, or they were pre-Socratics (pre-first-beginnings). In that sense, Heidegger's is a radically emancipatory ontology.