I liked that link. The idea that people do not reinvest all of their dividends, thus deviating from the model that one might have assumed, is helpful to understand.
Fwiw, I have pondered this myself verrry unprofessionally. It seems to me that equity does not have to match GDP growth because it is not the only asset class in the nation's capital base. Even if capital as a whole maintains a fixed share of GDP, particular asset classes within the broader category of capital can have different rates of return. It's not the rate of return on stock equity that needs to equal GDP over time, it's the return on all capital.
Consider the example where the national economy's capital consists of bonds and stock. Suppose that two thirds of the capital is in bonds and one third in stock. Suppose that bonds return 1% above inflation, stock 5.5%. What is the nation's return on capital?
.01(2/3) + .055 (1/3) = .025 = 2.5%, a very reasonable approximation of long term US GDP growth.