So wealthy people do not bother with housing, transportation or entertainment, and instead put all their money into investments? I think it's more likely wealthy people had income sources that allowed them to invest, while still enjoying some level of comfort.
I think it is reasonably clear from the GP that relative levels of investment was the gist; of course rich people live somewhere, moves about and try to keep themselves happy.
Then I don't see why it's important to state that those with lower incomes paying for housing, transportation or entertainment is the reason for their inability to become wealthy. Merely stating a difference in income causes the disparity is enough. Housing, transportation, communications, food and even entertainment are necessities.
That's because they have more money. You have to pay for the necessities, and then you can save. If you're making near minimum wage, you won't be able to save much.
Also, those investments, like stocks and rental properties, transfer wealth from the poor to the rich, generally.
Sure, no one is disputing the fact that rich people have more money than poor people. For many reasons the rich get richer at the expense of the poor, the OP was noting one of the reasons.
Another is that the tax code incentivizes making your income through investments, something unattainable for people who aren't rich.
