The point of the article is that if you clustered people based on genetic or anatomical properties in a non-post-hoc way, you would not end up with the same system of racial categories that are commonly used in the USA (or indeed any other country). As another poster has pointed out, the most striking example of this is the category 'Latino', which while often treated as a 'racial' category obviously has no biological basis.

This does not entail that no biological traits are correlated with race – biological traits are correlated to varying degrees with all kinds of subgroups of people. It does, however, mean that racial categories have no scientific basis.

To expand on this, imagine a Martian scientist studying human biology in isolation from human culture. Such a scientist would not subdivide humans into groups that match common racial categories, as these groupings are arbitrary from a biological point of view.