People get too hung up on the term itself that they flat out refuse to even consider what it stands for. I get it, I understand, reading an entire treatise is hard, dividing the term into very basic components and attacking their meanings individually is much simpler. That's what strawman arguments are for, after all.
Yes, "white privilege" is an extremely short-sighted name for it. It was first used to describe the structures of power established and perpetuated by (white) European colonists in conquered areas, so in a large part of the world "white" and "English" automatically put you in a better starting position and when the term was coined it, unfortunately, had "white" in it which always tends to raise a few hackles and get a few panties in a twist, in a "methinks the lady doth protest too much" way.
In America this were the WASP, white Anglo-Saxon Protestants, as the majority and ruling group, and the further you were from any of those things, the more of a disadvantage you were at. And since America once upon a time led the world in social progress, they chose a term fitting of their society, and it stuck.
But the structure exists in all societies. "Inherent advantageous slant in favor of a ruling class" would be better. Japan has their Burakumin, India has their caste system that formally "no longer exists" but come on. Eastern Europeans are discriminated against in Western Europe, non-Russians have it worse than ethnic Russians in Russia (so you can imagine how crappy that must be), the Han Chinese have it easier than Uyghurs in China; everybody discriminates against the Roma, and please, please don't embarrass yourself by saying the Irish had a jolly old time in England.
Oddly enough, nobody argues the above examples, but GOD FORBID you say white people in America have an easier time than the other races, or everyone throws a shit fit. As witnessed here.
"Privilege" is also a major point of contention here, people take it to mean you get handed a sack of money at birth and the most common argument is "I never had anything handed to me", with "there are poor [ruling class] people too, where is their privilege" a close second. Failing to take into account that even the slightest factor of inequality, iterated across a person's entire life, piles up. Nah. Probability is a nerd circle jerk that doesn't apply to real life, statistically significant factors are insignificant, and "the house always wins" principle applies only to casinos.
It would be better to say some people are "slightly less disadvantaged" than others, maybe that would be an easier pill to swallow, but probably not. People, by and large, are very reluctant to admit anyone in the world had it harder than them, and the "I started from the bottom / huh, we would be lucky to have had a bottom, I started in the bottomless pit" pissing contest is eternal.
So the question in the title is, can "non-whites" benefit from a socioeconomic system that is stacked in favor of a particular class/nationality/caste/race in their country/society? Yes.
