Everything you've said is on point, rich people mostly gamble to entertain themselves, they understand that gambling is risky so they can turn it into a habit that would attract addiction and make them lose wealth they've built for years or lose money while trying to make more when they can just invest their money and watch it grow on the long run.
What am trying to say is that poor people lack patience they're mostly very eager to make quick money and be like the rich class, they're willing to take risk at all cost forgetting the consequences, most poor people don't even mind risking the last cash on them just to make more.
That is also true.
Some times the poor people used to use the gambling as a quick rich scheme to rich quickly but in case of the rich poeple they are already rich so they play gambling for the entertainment and that's why the addiction rate wasn't that much high as compared to the poor peoples.
And there is another point for that the the rich people amount is low in case of gambling addiction rate and the casue is the rich peoples amount is also low as compared to the global population so that's why we saw the rich people's has the lower number in case of gambling addiction.