Rather than making armchair dismissals, consider looking at the paper and its citations which discuss the statistical methods used. From a cursory glance, it lo

Rather than making armchair dismissals, consider looking at the paper and its citations which discuss the statistical methods used. From a cursory glance, it looks like they use a standard model of how genes affect traits, which uses O(N) parameters for N genes, so the "curse of dimensionality" would not apply.