It's false, if a guy plays $100 and loses it in a casino the government will get a bit of it from the tax they collect, but if he stops playing it doesn't mean he will burn those $100, he will buy stuff with it and then the government will get VAT and the profit from the merchants who sold him the stuff.
Just because somebody stops playing with money doesn't mean that amount evaporates from the economy.
Why did you decide that these $100 will definitely be spent on something else? It is possible that a person will decide to keep them and keep them under the pillow, start investing or other options. Isn't that so?
I don't like the fact that the government interferes in all spheres of human activity, leaving no right to privacy. If I may say so, it is a jack of all trades.