I just came across it and though it seems like an obvious statement I feel like the rapport of cause doesn't apply here. Dying IS death and not a cause of it. Right?
Dying is the most proximal efficient cause of death. In one sense it is a process, and someone can be dying, but get rescued before arriving at death. So in some sense, there is a logical point here.
However, we do not tend to consider efficient cause a cause very often in modern thought, because we have a largely Alchemical/Newtonian view that conflates material and efficient cause -- the way things are is an immediate consequence of the way they just were in the preceding instant, and natural laws.
From so strong a notion of physics, someone is dead when they are dead, and to declare them to be dying before then is misreading their current state. You can never rescue someone who is dying.
Intuitively that last sentence seems wrong. So I am in favor of Aristotle's four causes (final, formal, efficient, and material) over Alchemy's three (correspondingly: mutable, cardinal, fixed (and even more fixed)).
I would assert that for philologic reasons, you are unlikely to care about this point if you are a modern English speaker. We have sets of triads of modal verbs (will, shall, and can; would, should and could; might, may and must) borrowed from the Germanic family, that map nicely onto the three causes (mutable, cardinal, and fixed). So we have trouble thinking of the fourth one, (the non-modal indicative?) as being separate from the third, and our traditional view of physics makes it redundant anyway.
(It may not be coincidental that Newton was an Alchemist, or that both he and Maxwell were English.)
While there is an undeniably an element of dying that can be identified in all cases of death, correlation is not causality. The "cause" of death is always a breakdown in the complex machinery of life.
To address @jobermark's comment, I didn't mean that to say that "breakdown in the complex machinery of life" is the "cause" of death. A cause must have some specificity that allows it be distinguished from other causes, otherwise it is merely a tautology that has no explanatory power. Thus one must identify what the breakdown is, and if that can be done with any degree of specificity, that is the cause of death.
My read of everyday English is that "dying is the process (or stages) that a thing goes through when it makes the transition from living to dead". With this definition, dying is not a cause of any sort. Various things can be the cause of death, and the general label affixed to the process that ensues when these causes arise is "dying". Thus, though a nice turn of phrase, the statement involves a form of category error.
A carpenter is the efficient cause of a table (Aristotle); the "building" of a table is not the efficient cause of a table. I'm using the idea that "building" is to table as "dying" is to death in this context.