The theory goes like this: under inequality, wealth is concentrated at the top. People at the top look to invest money, but spend a smaller portion of it compared to people lower down the distribution. This has two effects:
1. There is more and more money chasing after returns. This has a tendency to drive asset prices ever-higher. 2. Since the people who would spend the money (i.e., the less wealthy) don't have it, making returns becomes more difficult.
Warren's quotes in the article get at this, with the idea of earnings being decoupled from stock valuations, until suddenly they forcefully re-couple, so to speak.