This is hardly casting doubt on the nature of (human) death. This is purely a question about quantum mechanics, I'd say.
On a side note, I fail to see how the experimenter is supposed to survive with probability 1 in Everett's many-worlds interpretation and thus be able to distinguish the latter from the Copenhagen interpretation. Yes, there will be one world where he survives but in the "vast majority" of worlds he will be dead. (Disregarding for a second that counting how often the world bifurcates in the many-worlds interpretation is a somewhat delicate issue.) So in terms of probabilities, he will still die with absolute certainty as the experiment gets repeated infinitely many times.
The idea is that everybody else dies with certainty, from your observation point, but you yourself can't, because the denominator of the probability fraction consists only of those futures where you exist.
It happens to be a vivid idea to me, because a long time ago I read a short story that was more fantasy/horror than science fiction, but resembled it a little in spirit. It was about a kid in a small town who discovered that the grave digger for the town seemed to know ahead of time who would die, and dug the graves in advance. The kid thought this was just mildly interesting as long as it was just elderly people he didn't care about, until one day his parents were in a car accident and because one grave was ready, he knew one was going to die. He killed the grave digger and buried him in the open grave instead, and from then on, people stopped dying. Which turned out to not be a blessing.
It really doesn't have anything to do with souls or wanting to survive. The implications of this form of immortality are not comforting to contemplate.
These questions are pretty firmly metaphysical, and there's no reason to expect science will ever have an answer. There are an infinite array of unanswerable questions about supernatural phenomena that have never been observed and probably never will.
