Being White myself, I have absolutely no problem with the term "white privilege" being used per se. What's important is that it's used WITH CONTEXT.
Telling a White person how they are benefitting from white privilege is indeed relevant if it's addressing either one's actions or a larger systemic problem based on racial classifications. If a Black or Brown person is sharing an adverse component they've witnessed or directly experienced, it's absolutely critical that the awareness of that problem be linked to white privilege in a demonstrable way.
What's unacceptable (dare I say, even, RACIST) is weaponizing a White person's racial identity (via "The Association Fallacy"), as a reductionist talking-point or lacking context, in order to try to get the "upper hand" in dialogue or negotiation. If the author is referring to the term "white privilege" being misappropriated in this type of manner, then I definitely agree with her premise.
But the very real effects of white privilege aren't going to just magically disappear due to us expunging the term from our vernacular. So, instead, I look at the term "white privilege" in a very clinical and matter-of-fact way, going into a discussion -- and then humanize it when the evidence shows how BIPOC communities are being harmed by it.