I agree with a lot of what's written in that article.
Saying black people can't be racist is like saying women can't be sexist. Racism has/had/should have a simpler definition than what's being peddled as the popular one but I also understand why it's so.
The fact remains that there's a form of privilege to being white, non-black and lightskinned but this is only one aspect of life. There are other factors that may or may not affect that privilege in different situations such as environment, social status, background, age, education, etc. Things are really not always black and white (pun both unintended and intended).
Whether people call it racism or prejudice or whatever, it is still treatment based on the colour of someone's skin or their ethnicity.
Not every white person (who may reap the positive effect of white privilege if no other factors are present) has power behind them. Not every black person is powerless.
I know these conversations really are usually based on the western side of the world because I grew up seeing both powerful and powerless (mostly) black people and (some) non-black people. Therefore, I don't see a black person as automatically disadvantaged unless they actually are. Same with a white/non-black person being automatically advantaged.
But yes, due to the systemic racist structure, it's easier to say a black person has experienced racism but a white person hasn't; or a woman has experienced sexism and a man hasn't due to the prevalent patriarchal system in society. History backs one group up and not the other, in that regard. Can blame them though for holding unto that concept.