I don't think I can give a qualified dismissal of that paper but I am skeptical. They only examined the last 260 million years, for instance, whereas the Earth is 4,500 million years old. That's, like, 6% of the history of the planet.
On the other hand, I know other researchers over time have come to similar conclusions. There was someone in the '80s who proposed a similar kind of cycle based on different evidence.
So there might be something. There are plenty of cycles in the world. Why not a cycle of activity in the flow of material in the mantle?