Because of the difference on bankroll. Rich people have a huge bankroll that gives them freedom to increase bet or play more until they win huge amount while poor has only limited bankroll which they will stop immediately once they lose enough.
That's a valid point, the size of your bankroll has a huge part to play in contributing to he success of a gambler but on the other hand has its disadvantages too. Having a high bankroll also means you have more risk to manage, alongside having a huge and high bankroll you'll also need to have a good funds and risk management skill, else you'll loose more than you could've ever imagined.
something that is excessive or big is usually riskier, not just the money you have, even in gambling there is the same risk when a slot game has high volatility with a maxwin above 20,000x usually there is a big risk of losing large amounts of money to chase the maxwin while slot games with medium volatility have a maxwin of 5000x, it will be a little easier to get it and another example in sports betting is by choosing to bet on a parlay bet with total odds @1000, the risk is very big because you have to win all the matches you choose, whereas in sports there are always surprises and compared to smaller single bets, choosing to bet on 1 match with odds @1.5 will be easier to win.
example above that I mentioned answers your concerns about rich people who have a lot of money also having big risks just like these bets and actually winning cannot be measured by how much money you have but how lucky you are today.