Lead author Mohammed Sheikh believes that the existence of established power laws can help astronomers make sense of patterns in the dips in KIC 8462852's brightness. “This gives us an independent way to interpret the events and check consistency with the model,” he said in a statement.
Kepler didn't watch Tabby's star long enough to see many big dips, something various telescopes are working to correct, limiting the sample data. Even if the relationship is confirmed, Sheikh's work does not explain what sort of phase transition is coming or what physical processes might be driving it. The best the authors can suggest is it represents some sort of magnetic transition. Moreover, Sheikh's work does not incorporate, let alone explain, the claimed long-term dimming of KIC 8462852. This has not been measured precisely enough to study in the same way.
Since we have never seen an F type star behave like this, if KIC 8462852 is about to undergo some sort of transition, it will transform our understanding of stellar behavior – assuming we get to witness it. By the standards of a star that is at least several hundred million years old, an imminent transition could still be thousands of years away.