That's his point. Political categorizations seem arbitrary from a scientific perspective.

He doesn't say "arbitrary from a scientific perspective", he says "arbitrary". The former would be a silly point anyways. Would it make sense to point out how arbitrary it is that the houses of congress are divided up by party because party appears arbitrary from a (genetic) scientific viewpoint?

Don't confuse genetic/geographic science with science as a whole. Anywhere you can do experiments you can do science, and politics is no exception (although everything is much noisier). Certainly, the groups of people described by the census are meaningful in a scientifically confirm-able way: they identify with each other, forming clearly discernible self-selecting cliques, neighborhoods, etc.

I think his point was that race is often presented as a biological categorization, when in fact, biologically speaking, it is completely arbitrary, i.e. determined by factors completely independent of biology (specifically, politics, as you pointed out).

But even that isn't really correct, right? It's definitely true that the racial categorizations chosen by the census aren't great at dividing up humanity by genetic distance; there is probably a lot of genetic diversity in some particular race, while other races deemed distinct are nearly genetically identical. (And obviously, all humans are exceedingly similar genetically on an absolute scale.) But the the census races aren't useless or random biologically. There are plenty of diseases which have higher prevalence in some races than others. Whites are more likely to get skin cancer, less likely to be lactose intolerant. Asians are more likely to get alcohol flush reaction. Blacks are the exclusive sufferers of sickle-cell disease.

If he wants to say "the races as defined by the census are only weakly correlated with genetic distance or geographic ancestry", then fine. But that's a far cry from "the 'race' categories that are used in the United States are arbitrary...and do not correspond to any scientific view of geographical populations."

The author of the linked post has a entire book about the legal cases that set down these categories in the US. He does seem to think they are both arbitrary and bad (and somewhat unique to the US, unlike slavery and racism which are not a uniquely US phenomenon), in roughly the same way that a libertarian would object to everyone being pigeonholed as either a republican or a democrat since they believe themselves to be neither.

The author clearly has a problem with racial preference in college admissions. But this cannot be attacked by pointing out that racial categories are only weak biological indicators, because the justification for racial preferences is political and not genetic. And insofar as the racial categories are trying to capture the political dimension, they do a pretty darn good job.