After industrialization, a lot of people were able to leverage first-mover advantages and unrealized frontier opportunities into vast fortunes. But even then, having one extra dollar from daddy in 1790 meant having many, many more to give your own kids by 1820, even if you had 12 of them. That extra dollar might have meant you carried a full feedbag and got there a day before the guy who had to stop to let his horse forage, and getting there first was worth thousands.
Now, daddy's dollars might allow you to start from second place, and grow faster than the first-mover, who might be trying to bootstrap. Or you could do the same with investor money, but with corresponding loss of equity. If mommy or daddy fund you, you probably get to keep more of your own company.
As well the marginal utility of another dollar to someone who is already wealthy is low and they are less likely to use that money, whereas someone who is poor or middle class not only benefits more from another dollar, but is much more likely to spend that money in a way that stimulates the economy.
Those simply trying to avoid getting crushed by the system already know: "Them that's got shall get; them that's not shall lose. God bless the child that's got it all." If you want to get rich, you usually have to be rich. Making your first fortune is always the hardest.
If you aren't already in a position to invest anything--if you are living paycheck-to-paycheck or worse--the only way to own a robot is to build one, because you can't buy one. You can be outbid by anyone with a dollar that isn't already spent. You're already screwed. But you knew that, because you're pinching pennies so hard that Lincoln cries out, then the Lincoln in the monument on the reverse side squeaks out a protest. And if you do manage to build a robot, you'll probably have to sell it at some point for less than it its true worth, due to a crisis.
It even says it in the article. All you need to do to buy enough Amazon stock to retire is to already own a chain of grocery stores in New Jersey! Meanwhile, the employees of those grocery stores have to cut each other's throats to get an Amazon warehouse job, because that game of musical chairs took so many seats away all at once.
"Just own the damn robots" is a surrender to the zero-intervention inevitability of an ownership class that owns everything, and a dispossessed class enslaved to them economically, yet also almost entirely useless to them. Owning things is a solution that only works for problems that rich people have. It's advice maybe good enough for the top 10%, worried that they will backslide. It doesn't do anything for the bottom 90%, who either can't get ownership of a robot, or can't keep it long enough for it to solve their financial problems.
I don't think it's society's responsibility to look back further than the formation of that society. For the US, I think you can safely use 1776 as a starting point. The US formed itself with the express purpose of creating equality for the original settlers.
If someone is violating those principles, society should punish accordingly. If not, society is not "rewarding wealth". They are allowing for the fact that everyone is someone else's child, and that comes with it certain rights.