I think the argument is that, if an individual of a minority race does everything 'right' and still becomes a 'victim' of inequality in institutions (or application of institutional rules), then eventually the minority race is going to learn that they're damned if they do and damned if they don't, so there's no societal incentive for them to abide by society's rules.
One of the simmering tensions seen in some African-American neighborhoods is that what few shops exist in these neighborhoods are typically owned by Asians. There has been resentment that African-American's are more likely to be denied a business loan, and therefore are incapable of transferring their capital into a business that can then grown the wealth of the family, but the Indian or Pakistani or Korean can, and can do so in their neighborhood. This resentment can then lead to violence between the two groups, but the resentment is fostered by a system that plays favorites, which one could argue was a systemic inequality (which is, I think, what the article writer is essentially describing as white supremacy)