The amount of money you start with does not matter,as long as you have a good bankroll management and you know your limits. Obviously a rich person can afford to play higher stakes, take more risks, and win more money but at the same time he has much more to lose on the long term because he's got so much money. A poor gambler can only lose the amount of money he has, which is little and even if he ends up losing everything it won't affect him that much. If a rich person ends up losing everything to gambling, that would be a disaster for them and their life. Therefore, both rich and poor gamblers should be careful to gamble and risk only the money they can afford to lose.
I agree with everything said apart from the part where you are of the opinion that the winning of the poor are small so it will not affect him as much as the winning of the rich. This statement is not correct and should even be the other way round. The poor might be gambling with almost everything he has even though it will appear small and insignificant but the rich might be gambling with just a little part of his money even though that may appear big and can even be what the poor targets to win. I think losses affect the poor more than the rich, hence the poor should be very careful how much of their limited capital is put into gambling.