I have thought about this thoroughly, if have unlimited funds, I will not gamble. The reason is that I don't gamble for fun but to chase winning. My fun is always when I win something big, withdraw and spend the money. I take gambling as a serious business that can fetch me money and when you remove the money, there will be little interest in gambling from many.
That is what I also think: having infinite money means money is never a problem, and the reason why gamblers place bets is for the money. I know the fun can also be there, but if money were not involved in gambling, I know many gamblers wouldn't be into it.
I don't think you can simply generalize like this. You can defeat your statement with a simple example. Why do rich people place bets? It surely is not for money because most of them are losing money whenever they play. There are plenty of other complicated things involved in this process. Someone who gambles a lot will not stop tomorrow just because he received a lot of money from something.
If I had infinite money, I also would not gamble; I would only enjoy my money and look for other games that I don't need to spend money on. Gambling is a game of loss and win; I wouldn't want to lose money in gambling when I already have so much. Indeed, gambling is a business. People are more interested in it because of the money, but they always pretend as if the fun in gambling is the most interesting thing about it.
I like how we all say this but I wonder whether we could actually stop.