"This means that these infintesimal mixings have even less impact than you'd think. A modern Japanese person could have a European ancestor who traveled to Asia a thousand years ago, but have zero genes from that ancestor. Which means that while that European is technically an 'ancestor', this is just a bit of historical trivia, it means literally nothing about that Japanese person's biology."
It also means that a modern Japanese person has thousands of "Japanese" ancestors from whom they received zero genes. Of course, this is a bit of misdirection, as the genes that one receives are not unique, but drawn from a pool of possible genotypes common to humanity. The matter of how closely we resemble each other is not one purely of ancestry, but of the size of that pool - our overall genetic similarity. From what I gather, it's not an exceptionally large pool. I may not have gotten whatever gene controls the formation of the human prefrontal cortex from the same nth ancestor as you, but I got it all the same.
Also, where does dominance play into this, I wonder?