I wouldn't put everyone under this category, there are levels to this, some people gamble with little amounts of money so we wouldn't consider them to be rich exactly. Gambling is only expensive by choice, some people make it very cheap because they gamble with what they can lose easily without being bothered by it, just because people gamble it doesn't mean that they are automatically rich.
It doesn't necessarily matter the amount anyone can put in to gambling to be qualified for this category op is talking about and in since it only advisable to gamble with an amount we can afford to lose and considering the fact that we have different individual financial abilities such that what might be small for me might be big for the other person, we should only bet within our own financial circumstances. However, relating to what the op said I will suggest that only those who gamble with Left over money after ensuring their basic important needs are well taken care of should only be categories to this level of I am rich because gambling is my entertainment.