The article misses a keyword - RISK or risk tolerance.
Rich kids are able to take MORE risks than poor kids. We know that risk taking is positively correlated with wealth.
Both rich kids and poor kids take risks (financial and otherwise) get different results when they fail and when they succeed.
Simply, the rich kids suffer less from financial failures and make more money from their financial successes.
FAILURE
The poor become fearful after a few failures. Then over-compensate (by being wasteful spenders as mentioned in the article) or under-compensate (stick only to absolutely safe paths - bad in the long term)
A loss of $10,000 might get only a shrug from the rich kid but the poor kid might go mad with depression and suicidal thoughts.
SUCCESS
Finally, let's look at what success means to both classes. If we look at money as leverage, then even financial success between the rich and the poor is completely different.
Let's look at what a $0.1 increase in a stock price means to the two classes.
Person A has 100 stocks - $10 profit. Person B has 100,000 - $10k profit. Same investment. Both succeed in the same stock but result is completely different.
Writing this has clarified one point for me. The poor need to risk a larger percentage of their networth to see sizeable returns on their success.
When wins don't feel like wins and losses are devastating, it creates apathy towards trying.