This is well-known in ethics, but not as a flaw of argumentation, rather as the problem of causal resposibility. The problem is thorny because drawing the line depends on resolving highly controversial issues in ethics and metaphysics, free will, attribution of agency, efficacy of proximate vs mediate causes, etc. Sartorio's Causation and Responsibility and Del Coral's Social Commitment and Responsibility are recent works that discuss it.
To see why deciding what does or does not count for responsibility is challenging recall that there are causal chains connecting any event to multiple past actions, by people and not. Where in those chains, and how, do we place the responsibility or blame? Is this placing somehow objective or does it entirely depend on social conventions, context-specific interests, etc.? How much of responsibility/blame goes to various links in the chain? If one accepts causal determinism it is not clear that the blame can be apportioned at all, as Del Coral points out:
"...by analysing the causes of the agent's actions, we pass the buck backwards and relieve the agent from her responsibility. The buck would stop by showing that the agent acted freely (this is, she could have chosen not to act). Determinism and free will, enter into conflict."
Even if we accept free will or some form of compatibilism, there is no consensus (or even majority) solution to the resposibility apportionment, and therefore there is no sure fire way to resolve even your example. Here is one way, sketched by Valentyne:
"To be agent-responsible for an outcome, the agent must be causally responsible for the outcome and the outcome must be “suitably reflective” of the agent’s autonomous agency. There is much debate about what exactly determines when an individual is agent-responsible for something, but it’s clear that one can be causally responsible for harm without being agent-responsible for it.
Presumably, your cousin's death is not “suitably reflective” of your intentions for you to be held responsible for it. This reliance on intent generally guides common-sensical and legal assignment of responsibility. But it is not without its pitfalls due to the general obscurity of "intent", and the phenomena like transferred intent, willful ignorance, irresistable impulse, etc.
And under some ethical positions you do share a portion of the blame, say because you failed to resolve your gambling problem, and knew, or should have known, that it might put people who care about you in harm's way. This would be a case of "absence causation", responsibility for inaction/omission. This notion is problematic even in more straightforward examples than yours, as Sartorio points out:
"If we were to say that my failure to water a plant that I promised to water is a cause of its death, then we would probably also have to say that the Queen of England’s failure to water the plant is a cause of its death (because it is also true of the Queen of England that, had she watered the plant, the plant would have survived)."
But there are responses to such skepticism. Woodward, for example, exempts agents without a serious opportunity to act, which would exclude the Queen of England. But I am not sure if it entirely rules out the blame in your situation. In the legal system there is a notion of "felony murder", which classifies accidental killing in the commission of another crime as murder, even when the person did not even physically do the killing (but, say, an accomplice did). It is of course a long way from your scenario, but is there a difference in quality or merely in magnitude?