A pattern in nature or just coincidence?
Probably coincidence, since 27 million years give or take is a fantastic range of time but journalists and professional doomsday prophets are making something of it the way they do Mayan calendars and Biblical numerology. When it comes to real concepts of time, 66 million, 26 million, and 27.5 million don't have much in common.
Yet the paper does link them as non-random events, using the bane of informed food and chemical acceptance of science - statistical analyses.
They declare that extinctions followed a similar cycle of about 27.5 million years - but that means we are really only talking about two. And accepting it requires a daisy chain of other speculation that will make Occam pull out his Razor, like that asteroid hits also follow a pattern. And Monte Carlo simulations? I get their value but come on, if I am at Intel and you tell me we are ready to spend $10 million to tape out something and your data are Monte Carlo simulations, you are fired. It is truly "academic."
A lot of the discussion around this may be the plague of narratives in the 21st century - teleology - where people want to find a pattern that matches some purpose or another and match events to it. So match the data to a broad range of time, then find someone else who speculates asteroids also appear in a cycle, etc.
Work hard enough, and you can link it all to Bilderberg. More likely is a geological mode of action that they discuss but are definitely not known to happen in any astrological cycle; flood-basalt eruptions, which is to say volcanoes.
Volcanoes can cause acid rain of the kind 1980s environmentalists lobbying to ban hair spray only fantasized about. Nature can create huge variations in temperature, in radiation from the sun, in CO2; all things we try to blame on anyone without a Prius. But they don't follow a consistent pattern. So there is a common denominator among extinction events but it isn't a time cycle. It is that the natural world is out to kill everything it can, and in eight instances succeeded.