This is all they did:

We define displacements as students who enrolled in a selective college, but had a composite SAT score below 1250. We define replacements as students who had not enrolled in a selective college, but had a composite SAT score at or above 1250.

They basically picked an SAT score of 1250 and then just threw up the ethnicity of students from the High School Longitudinal Study of 2009 of 23,000 students who were above that score.

So while asian students might get better grades or benefit from affirmative action in many schools (in some high profile schools the opposite is true), apparently they aren't crowding higher education because their test scores are markedly superior. While they are still overrepresented, their numbers go down because more asians with lower scores are getting into top schools (or were, in 2009) than are excluded despite top scores.

I don't believe for a second that a racially blind criteria would cause asian enrollment to go DOWN.