I think you have said everything about the reasons why gamblers prefer to stop gambling when they get old, financial balance is the most important and that is the main reason they stop so that their finances remain balanced considering that old age is a time when you are no longer able to work to earn money like when you were young, all of that is done because there is also responsibility.
On the other hand, I might also be able to add another reason that the mindset of someone who has reached old age is also very likely to change, usually they will stop an activity or habit if it does not have a positive impact, old age is an age where a person's mindset is very mature.
If this activity is only done for leisure purposes or to pass their time, I believe they won't stop doing this activity. But if in case this is already affecting their financial budget, then, high likely that they will stop doing this heading to their old age as they would want to save their money for retirement.
A gambler don't have to stop from gambling when they getting old. They can stop gambling forever anytime they want and the important thing is that they realize that they already playing gambling for some time and it is better they focus with their future. Many reason that they can have to stop gambling even before they old so they can see that life is not just for playing gambling but they have many others things that they can do. But yes, when someone getting old, he will have cognitive decline, memory loss, and can not focus on what he will do.
If he can realize that thing, he can thinks about stopping his gambling activity before he getting old. That will much better for him because he can use his spare time by doing other things that can gives benefits to him. Maybe people needs to think about that so they can realize that stop gambling will not makes their life ruins.
If you know that you are only doing this for leisure purposes, and you are not having burden with the money spent on this activity, then, I believe you can do this activity as long as you can. And as you said, if the person has other things to attend to like doing other worthwhile activities , then it is his prerogative to do so. So long when you reach at that stage, you are already enjoying at what you do and not because someone is pressuring you to do such task.