It's a little more technical than this paper, and presents very well why removing discrimination in algorithmic decision making is a complex task.
If I'm understanding the authors correctly, they're saying that blind algorithms don't have equal outcomes by race -- so they're reintroducing race to the algorithms so they can adjust for disparate outcomes.
Basically they're arguing for affirmative action algorithms.
the race-blind models aren't necessarily really race-neutral; they could implicitly have something like "affirmative action" in either direction, and reintroducing an explicit race variable could be the only way to get rid of it. or the opposite might be true! it takes real care to get this stuff right whether notion of equality you aim for.