Think about what this means People who have, say, three black great-grandparents and five white ones, will vary widely in how black they look, and this likely affects how they identify. But there are also invisible markers of ancestry - of the sort you would expect maybe were visible only on an X-ray if you looked carefully. Those could easily break the other way. You could easily get someone who looked white (and thus, probably identified as white), but were "black on the inside", in terms of their less visible characteristics.
Yet the algorithm sees through all that, and manages to see what you feel like? Correctly classifying Shaun King as black and Tom Jones as white? From a 8x8 X-ray picture?
The people who insist that "race is real" should be the most confused by these results, since we know how fuzzily identity is coupled with ancestry, especially in the main groups studied here, black and white Americans.
I'm much more prepared to believe, for instance, that there is something catastrophically bad going on in medical image dataset collection, than I am that self-ID race is nebulously predictable from almost nothing.