I mean that's the basic gist of it anyway. The poor gamble because they feel like they need to, the rich gamble because they can. Plus as I said in a previous comment I made that certain gambling forms like sweepstakes and lotteries are literal money traps that are made to lure poor unwitting people into playing, they paint the picture of a better life if you win the game and claim the jackpot, but we all know that's far from happening considering the whole system's rigged against the player. Still, since these poor people, most of the time uneducated and desperate to get their big break in life, fall victim to these traps where they constantly spend money, some of them even dedicating a portion of their salary to pay for tickets and shit. Can we do something about it? No, not really.
If I may assume, I do not agree to generalize that poor people feel the need to gamble, I think all factors are affected by the environment. not all poor people like to gamble, only some of them hope to win a victory from their gambling session. in a sense, getting rich in one night. and the only type of gambling that makes someone a millionaire, is lottery gambling. Lots of gamblers hope to get the jackpot from the lottery. even if it has to be percentaged, the probability of winning is very slim. only lucky people once in a lifetime win the jackpot from lottery gambling. but make no mistake, if there are some rich people who also like this type of lottery gambling.
btw, I'm intrigued by one point you said, "the whole system is rigged" I don't know how you knew that was the case. for an illegal casino, it is highly likely that cheating could occur. but for reputable casinos, which have a credible reputation. less likely, if they commit fraud. logically, they don't want the reputation that they have pioneered to be destroyed immediately because the casino is suspected of cheating.
For the rich, yes it is true they gamble because they can afford it. yet it makes no difference to the casual gambler and even the poor gambler, that they are potentially addicted. the difference is, they have a source of funds even though some of them have gone bankrupt because of their gambling. it could also be, they are just gambling for fun, after going through a series of busyness in their business.
anyway, for the most part we agree with what you said even though not completely.