TL;DR Asians are "the new Jews" and are discriminated (often implicitly) - for example they ace at high-school STEM competitions, yet they don't make that many undergrads as they should (with a notable exception of Caltech).
Gelman says in that critique that he agrees there is an underrepresentation of Asians.
That's not actually Gelman's analysis. He's just relaying some criticisms that were sent to him by Janet Mertz. Ron Unz responds to this, corrects some of his own errors, and shows his claims still hold. Then Gelman (proxying for Mertz) and Unz go back and forth way too many times, using way too many words and almost no data.
Eventually Gelman gives up, so Unz moves on to reviewing Mertz's old work. Let's just leave it here: http://www.ronunz.org/2013/03/16/meritocracy-dangerous-cance...
The author suggests that top Asian students are being discriminated against (implicitly or explicitly), and it's unclear whether top non-Jewish white students are being discriminated against, or whether they apply in much smaller numbers to the Ivies.
In the article from The American Conservative, the claim that Jews are over-represented is rather hard to miss.