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.
Taking risks involve you making a choice that may prompt you fast response more especially when you're aiming at something but clearly it stands that you should risk what you can afford to lose, that way you're on the verge of no regrets but maintaining a responsible gambling lifestyle. Therefore i would gladly concur to your opinions about what taking risks responsibly meant.