inequality? confusion...

The author of the video conflates income and wealth-- a big no-no. More important: He confuses "ideal system" with "ideal outcome"-- implicitly discounts decisions, as if individuals are largely powerless within the system.

Along those lines: This makes (a lot more) sense if Dave Ramsey is right that most people are broke-- not because of what they earn but what they spend/save. (See also: who owns your home if you have a big mortgage?)
Another angle: to the extent that (govt) Social Security provides an implied (albeit lousy, jacked-up) nest egg, this should be included in "wealth".