Some rich people may be more disciplined and can adapt and increase their funds quickly because of it. But this doesn't mean that all rich people are like this. There are those who make trivial money management mistakes, take too much risk, or even fall into tilt. This can be the case both with those rich people who are addicted to gambling and those who trade futures with leverage.
More risky people can quickly get rich, but then they can also quickly lose everything they managed to earn, or win in this contest. Systematicity and discipline will help to save what they managed to earn, because such people are less inclined to risk and rely only on their knowledge and not on some kind of chance or random luck. So you can't compare all rich people, they are also different and got their fortune in different ways.
Rich people do not always gamble risky, some gamblers gamble based on a certain allocation. The symptoms you mentioned are correct but I think they have the potential to take risks and the ability to take risks. They can take risks in gambling because they have more wealth than the poor and they are ready to take risks and even if they lose that amount of money they can easily recover from alternative income source. Just as poor gamblers gamble to make money rich gamblers gamble for the purpose of making money and for entertainment.
As you said in the last paragraph, there are many gamblers who take care of themselves differently and don't gamble excessively. There are a few who are defensively involved in the gambling industry and continue to gamble regularly.