I'm not sure of the relatives, but it affects the close ones for real. I personally experienced it. Being into gambling I've suffered much and now I've come out partially. At times the loss can't be accepted and our minds won't work as we think. This affects the family and the close ones. They can see the difference and the same makes them down. Atleast to keep our surroundings happy we should have healthy gambling habit with limits.
Usually nothing you do in your life has influence on distant relatives. I have cousins that live in different countries. Sometimes we see each other once a year, sometimes every 2 years... If I died the only way it would affect them is that they'd have to come for the funeral. About what OP wrote, most of it is obvious. Yes, your lifestyle affects your family, but it's always like this, no matter if it's positive or negative. A person who goes to prison for a crime will affect the family, someone who overdoses drugs will, and so on, so forth.
It's important to not be selfish and notice what's going on around you.
Whatever we do affects our society, and when one is addicted, he has affected the life of few people in the society. Every road lead to the end of the world. Addiction can increase in a society if one influential person who is addicted influences the people around him. That's why to make a change, we must begin from ourselves. However, the distant relatives, have nothing to feel sad about if they weren't present in the time of occurrence, didn't hear the news, showed no effort to solve the problem, and didn't contribute in any way to solve the problem. Those who had personal encounter with the trouble and helped the person out of the addiction, will remember the incident, in what seems to be a long time. Those thoughts can affect the person in many ways, but it's his responsibility to bypass the reasoning and focus on their daily tasks.