From the article:
> “Under our constitutional structure of separated powers, the nature of presidential power entitles a former president to absolute immunity from criminal prosecution for actions within his conclusive and preclusive constitutional authority,” Chief Justice John Roberts wrote for the court. “And he is entitled to at least presumptive immunity from prosecution for all his official acts. There is no immunity for unofficial acts.”
There aren't just 2 types of acts. There are 3: constitutional, official, and unofficial.
As such, the phrase "exercise of his core constitutional power" is significantly less straightforward than it might seem at first glance.
If you read through the ruling, a lot more questions arise than answers. And Sotomayor's dissent only highlights how they don't know themselves. And it's not as though it was clear before this ruling. It was unclear, and this ruling says very little in practice.