This essay presents interesting comparisons and data, but then it goes on to try to explain that the top 0.01% are getting richer faster because they have special skills and technologies (such as being able to scale a business up using foreign workers, or manage 20bn assets because of computers).
What is not mentioned but certainly plays a key role in one's ability to perform so well financially is the special opportunities the top 0.01% have and circumstances they operate within compared to the lessers. If we were to review each person in the top 0.01%, I expect most of them would be making their huge gains not by exercise of special skills but rather by exercise of special circumstances.
RISK - As we have seen with the 2007/8 financial crisis, there is a small group of very wealthy, very powerful finance people who can take enormous risks with other people's money, profiting whether they win or lose. The 07/08 crisis cost the general public (in bailout using public funds (debt)) hundreds of billions of dollars. But the stratospheric executive bonuses paid to fund managers and bank executives during the lead up years was not retracted. So the people that took unreasonable risks profited greatly, and the public paid for their profit and then some. Even during the following years, the executives and fund managers received significant bonuses. And thanks to golden parachutes, the exit/firing of some of them resulted in even bigger profits for that group.
OPPORTUNITY - The wealthier one is, the easier it is for them to get credit. Even in cases such as Trump where he has a long history of running businesses into the ground and leaving debtors unpaid, he was famously able to secure very large loans to take even bigger actions (which similarly often resulted in underperforming businesses which would later seek forgiveness or reductions of debts). The point is, once you're rich enough, you need never risk your own money. You can borrow huge sums to seize opportunities. When you win, you win big. When you lose, you can probably get away with no personal loss.
LAWS - With wealth and power comes influence. You can afford to lobby (sometimes a polite term for bribe) to get special laws or loopholes that have direct financial benefits for you. Perhaps it relates to a defense contract, and you hold a lot of Boeing stock. Or perhaps it relates to an FAA regulation and you hold a lot of Boeing stock. Or it's a special rule that lets you write off the purchase of a piece of luxury property as a business expense.
TAXES - This is a huge space for gaining an advantage over the normal people. Not only do you have the means to play the offshore/shell-company game (reducing your tax burden, perhaps to zero), but you also can do strange things like deferring your taxes indefinitely if you're a hedge manager.
I could go on with plenty more examples of special advantages that the top 0.01% have compared to everyone else. These advantages, even if modest, represent an exponential benefit in terms of financial growth over time.