That blog post looks highly suspect to me. The AEI is reposting the work of a blogger who has taken data from two different sources: a paper on the GINI of individuals, and GINI as calculated for households and families by the CBO. There are two big problems I see:

The data on families and households includes capital gains, but the data on individuals doesn't (it includes only regular income). He hand-waves that away by saying, without proof, that capital gains are proportional to income, so that part doesn't matter. Given the differences in how we tax income vs. capital gains, I think excluding them from a GINI calculation is a big deal. Frankly I could simply interpret his chart as showing that rich are increasingly moving their gains away from income and towards capital gains to avoid taxes.

Second, for his graph of GINI for individuals, he's picked the GINI only for people that have an income. So again we're not comparing the same kinds of numbers. In that same paper, the one that includes everyone (not just income earners) shows increasing inequality in the last 30 years.

The idea is an interesting one: is the way we're structuring our families and households leading to increased income inequality? But unfortunately, the data he has is not good enough to show us one way or the other.