The article is a very good effort on David Wong to try to explain privilege.
The article, insofar as it makes philosophical claims, is piss poor. It is "some Rust Cohle shit", because it's on an intellectual par with the shit the writers of True Detective came up with.
Had the author cared to actually read into the philosophical literature, s/he would have learned what it is to be a person is a question of ethics and personal identity- to say someone is not a person is also to say that they do not possess moral personhood, which is what makes it wrong to treat you as an end to a means, or to painlessly kill you in your sleep.
Being determined in no way undermines the capacities we think entitles someone to moral personhood- i.e, an interest in certain states of affairs obtaining, a sense of self persisting over time, autonomy, self-awareness, etc.
Further, he conflates determinism with eliminativism about personal identity. To say that I have no identity because of the necessary succession of events that led to my existence is patently false.
The claims about shared responsibility are overstated. There is significant controversy over whether someone is differentially responsible to members of another community their ancestors oppressed. Michael Sandel argues for this view (in my opinion unconvincingly, but without doubt skilfully and thoroughly) but it is extremely distant from being a "simple fact". One competing view, for example, is that whoever is most able to remedy injustices at any given time is most responsible for remedying injustices at that time, and there is no differential responsibility beyond this.
One should also note that this is partly a debate between communitarians-like Sandel- and cosmopolitans. This is not a debate between progressives and reactionaries. Whether or not you subscribe to communitarianism, you will generally be led to the answer that whites are de facto responsible, merely because they hold all the power, and not because of historical facts about how this power was obtained.