I've seen that video in the past, and it bothers me tremendously. Because there are a lot of accurate facts coupled with ominous music, but it never actually proposes why wealth inequality is a bad thing, in and of itself. It preys on our instinctual idea of "fairness" we all had as children to garner an emotional response: He/she got a bigger cookie than me, we have to share! Not really valuable info to act on.
To me, nominal wealth inequality means nothing as a stand-alone measure. You mention "sustainability," which could be a real concern, but I wonder how is it a concern? Just showing that there's a lot of wealth at the top and little at the bottom does not necessarily imply that the bottom cannot live a decent life or that there is not enough economic activity to allow continued growth of the overall economy. Nominal wealth is just not logically connected to those things.
Think of my definition of "middle class": If it could be shown that the bottom of the ladder has no chance of climbing up, that economic growth cannot continue because the top has all the money and doesn't spend it, and/or that quality of life gets worse and worse for the bottom, that's a concern. But the truth is, quality of life (measured by goods and services available, anyway) is better at all levels now than it was in 1976 - the year the video talks about in reference to CEO money. Wealth inequality has grown, but it has had no obvious detrimental effect on the lifestyle of the poorest among us.
The other thing that bothers me is this: The only time the video mentions any metric other than "this feels wrong" is when he mentions that the CEO is paid but does not work 380x harder than the average worker. But we aren't paid based only on how hard we work. We're also paid based on risk, responsibility, and negotiating power derived from special in-demand skills, among other things. Try imagining a world where people are paid based on how hard they work. It's horrifying: First, you've got the problem of measuring "how hard." Even if you pretend there's a way to accurately do that without extreme bias toward those who could present the best argument (probably those who could afford the best lawyer!), you run into the problem of all kinds of perverse incentives. It's probably "easier," by many measures, to develop a new operating system than to shovel horse shit all day. But I'm glad Bill Gates worked on building up Microsoft rather than becoming a highly compensated pooper-scooper.
Also, I hope this doesn't cause this forum's first case of silly internet flame wars. I have the utmost respect for you and actually enjoyed that post when I read it, back when you published it, because at least it made me think! So thanks for your input on this slightly-off-topic-but-very-interesting point!