I think responsible risk is the same as only using money that we can afford to lose.
If we can only afford to lose $200 a month then only use that, there is still a risk of losing it all but if that happens it will not affect anything, because that is the amount we can afford to lose.
But it could also be for other gamblers responsible risk is how to use the money to gamble, meaning with a small capital then will play casino games with low volatility, or when betting on sports betting set a small betting percentage to suit the budget.