> Why are you using that set of genes, instead of a different set
The study in question (doi:10.1016/j.ygeno.2010.07.004) used ~250,000 SNPs, because those were the genes measured from previous studies. Even if all the SNPs in the human genome were used, the clusters would remain or become more pronounced - that's how principal component analysis works.
> or a measurement of 'height in cm' or analysis of ear-shape?
Why would you measure anything other than genes if you're measuring kinship? Genes are inherited, height is affected by nutrition.
> And where is the cut-off for a cluster?
There is no unambiguous cut-off - that does not mean the clusters don't exist or have descriptive value.
> Do you find it in any way strange that someone from the Netherlands and someone from Greece are the same 'race' even though, on average, their skin-tone, eye- and hair-colors, and heights are strikingly different?
Genetic maps tell us the Dutch and Greek person are more closely related than the Dutch and Japanese. Whether or not it's strange that their heights vary widely is irrelevant. I'm closer in height to my friend than to my sister, yet it's not strange that my sister is part of my family, while my friend is not.
> but the classification of people into distinct 'races' is arbitrary.
Tell a clustering algorithm to find ~5 clusters in the human genome distribution, and those clusters will correspond to traditional races. That alone should tell you it's not completely arbitrary, though you are right that the precise boundaries are ill-defined.
What is somewhat arbitrary is the choice of ~5 clusters - why not 10 or 100? That's simply a product of in/out-group organization. When you're interacting and competing with humans across the globe, as is the case in the modern world, you group up along the coarsest scale, or be out-competed by a bigger group that's less divided. If you don't group up at all, then that's no different than being a group of one - even the smallest team will out-compete you.
This explains the article as well - people in the past were more geographically limited, so they formed groups based on those local differences, instead of global ones.
If you have any more questions, I'd be happy to explain.