I don't even give most of them this much credit. Because if they want to refer to white supremacy or white privilege there are already terms for that. I think "whitness" is just a conveniently vague cudgel to win arguments with.
As the academics at the beginning of the article show, it can be used to describe anything you want it to, because it doesn't really describe anything. And if you don't like it, well you just "don't get it", or you're "fragile". This kind of language game is becoming standard across a whole range of social issues.