I enjoyed this video, but I have one problem with this argument.
This assumes that everyone follows this same argument of egoistic altruism. The gains by everyone ensuring that everyone prospers make sense mathematically, but socially you'll never have that happen unless forced.
You end up with a prisoners dilemma situation.
The only feasible way to this is to force/persuade the top earners in a society to give to the bracket below them until that bracket can contribute to the bracket below them. Once that bracket can give, you move on to the next bracket until everyone is covered.
It's hard to see this happening.