The author is correct. Race is a social construct. It is not biological.
DNA reveals where some of our ancestors lived, e.g. specific continents. It does not reveal our national identity, or native language, or ethnic features generally.
DNA identifies sex. Sex is biological. The concept of gender is a little different. Gender is really a linguistic tool. But it has been applied to behavior associated with male or female identification. For example, culturally we associate dresses with females. (And kilts may seem odd from outside a culture where they are seen as appropriately masculine.) There is nothing intrinsically feminine about dresses versus pants.
What I find bizarre is that this media revelation about Rachel Dolezal has been reported by right-leaning news outlets as if race is a biological reality. It has been reported on by left-wing media more correctly as a social construct.
Have conservatives now embraced the concept of biological race?
To say that race is only a social construct and not biological presupposes a definition of race that I do not think is shared by average people in ordinary circumstances. I think that by using the term “race”, people are mainly referring to appearance and ancestry. Skin color and texture, hair color, eye color, facial characteristics (lips, nose, etc...)... are all determined by biology. It is true enough that there are Indians darker than any African-American and all kinds of other such situations that can cast into doubt the usefulness of dividing up a population by race. But to say that biology is not the driving factor in a person’s appearance, what we commonly understand as “race” and that this biology is not passed down from generation to generation does not make a lot of sense.
All that said, the important thing should be that we all human beings equal before the Almighty. But trying convincing a liberal of that.