It is at least true that, in the cases where a gene for pigmentation is simple Mendelian, the darker color is usually dominant over the lighter color. But like every rule in biology, there are doubtless many exceptions, cases where some genes show mixed dominance, or where the light color is dominant over the darker color. And that doesn’t say anything at all about genes for traits other than pigmentation.
Frequency of specific genes varies for groups who are self-identified as “black” or “white.” These genes include everything from stuff that makes you look different to stuff that makes your physiology different to genes that have no identified mechanism at all.
The reason for this disparity is the history of human migration and the fact that, as evolution alters genes and relative separation alters the frequency with which those genes appear in descendant populations, the average makeup of a given gene pool changes.
The decision to create a category of “black” or “white” is arbitrary. Lumpers and splitters can create many other types of categories including ones such as haplogroups.
The propensity for unions between any two individuals from any (arbitrarily-deifned) source group, along with the increased mobility of the modern world, smooths out (but does not erase) gene distribution across historically separated source groups.
A crude analogy might be drawn with automobile product lines. One might see average differences between a Ford and a Fiat related to the components which make them, but there is no individual component that absolutely guarantees a given car is a Fiat, a priori of proving exactly where that component is made and checking all Fords to make sure no Ford ever has it.
There is no “black” or “white” gene by definition since these groups are self-identified, but the gene pools themselves of these two self-identified groups contain clusters of genes the average frequency of which is different between those two groups, and it is this average frequency difference that underpins many of the observed differences be they appearance or physiology.
I might suggest here for further reading.
Malik’s book Strange Fruit is a more complete presentation.
He answers your question this way:
“There are no genes that are specifically ‘black’ or specifically ‘white’, but some genes will be more prevalent within black populations and some more prevalent within white ones. And that is sufficient, race realists suggest, to divide the world into races. We know, for instance, that Europeans are more likely to have blue eyes than Africans, and more likely to be taller than East Asians. There are also less obvious differences between the races. If you are African, for instance, you are twice as likely to have a twin brother or sister than if you are European. East Asians are half as likely again as Europeans to be born as one of a twin. The fact that there are no pure races does not necessarily mean that there are no races.”
He has a much longer explanation of why “race” is sort of a lame concept, and I recommend reading the whole piece, if you are disinclined to purchase the book.