"Easement" isn't a magic word that let's the government use your property how it wants. (And no, the government can't just force you to run a public park on your property; governments have to buy the land they build parks on).
There is an easement here--it's the right of way that arises allowing the public to cross private property in order to get to the sea shore. If that was what the litigation was about, Khosla would definitely be in the wrong. But the state is going way beyond that--it's forcing him to keep open the parking lot, allow access to the beach above the mean high tide line, etc. That goes way beyond the easement that exists.
And the state admits that. There is no dispute in this case that the parking lot and sandy beach are not part of the easement. That's why the state had to go through a backdoor route: they're saying that he can't change the use of his undisputedly private property without getting a permit to do so.
I don't know the extensive history of the case, but from what I surmise it's because the lower court punted on the Constitutional question. The Supreme Court case law we have says that takings may happen when, e.g. denial of a permit prevents you from doing any development on your land. Here, the state is demanding that he apply for a permit to change the level of "access" at the beach. The lower court had said that the takings question was unripe for review because he hadn't applied for and been denied the permit. Khosla refuses to get a permit, and argues that requiring a property owner to get a permit just to change the use of the property is itself a taking.
If he doesn't get cert based on the current petition, will he have the option of applying for the permit, having it (presumably) be denied, and then trying again?
There is an easement here--it's the right of way that arises allowing the public to cross private property in order to get to the sea shore. If that was what the litigation was about, Khosla would definitely be in the wrong. But the state is going way beyond that--it's forcing him to keep open the parking lot, allow access to the beach above the mean high tide line, etc. That goes way beyond the easement that exists.
And the state admits that. There is no dispute in this case that the parking lot and sandy beach are not part of the easement. That's why the state had to go through a backdoor route: they're saying that he can't change the use of his undisputedly private property without getting a permit to do so.