The article about these papers does not present a mechanism that would account for the Hayflick Limit.
Nor does it explain why dogs, for example, age and die more quickly than humans. If there is a mechanism of epigenetic drift that would explain this, I do not see it in the article.
The obvious answer to senescence is that we are programmed to do it. Cells die when they are supposed to die; if they don't, we have a problem.
Likewise, mammals die when they are supposed to. It takes less time to train a puppy to survive on its own than it takes to train a human. Hence, dogs are optimized to age and die more quickly. It's better for the species.
If we were not programmed to get old and die, evolution through natural selection would not work. We would never adapt to changing environments and our species would fail.
Aging and death is not an accident or a deterioration from damage or a drift away from a correct instruction set. It is an absolute hard necessity, without which we would all be long gone.
Stop wasting your time on nonsense articles like this and seek the mechanism that provides us as a species with the flexibility to adapt. Until we see aging and death as an core mechanism, we're going to be looking in the wrong place.