The island has largely been owned by one person or entity for 150 years, starting with Walter Gibson, who first bought up most of Lanai as an individual. His holdings ended up in the hands of the Hawaiian Pineapple Company which was essentially owned by one person, James Dole. Castle & Cooke (a corporate entity) ended up acquiring the Hawaiian Pineapple Company and renamed it the Dole Food Company. Eventually, Dole split its real estate and food operations into two companies, one with the food operations and one a real estate company. The real estate company was given the Castle & Cooke name and it was taken "private" by David Murdock. So while its technically true that Castle & Cooke, which is the seller, is a corporation, its really just Murdock. And while the reports are that Ellison is taking over ownership of the property from Castle & Cooke, its not clear at all that he's buying just the assets (the land) or if Ellison, in effect, is buying Castle & Cooke. Even if Ellison is just buying the assets, I wouldn't be surprised in the slightest to learn that he had set up a company to hold those assets rather than is buying them to be held in his own name as an individual.
The pineapple plantation was shut down in 1992, before the spin off of Dole Foods and Castle & Cooke and before Murdock took C&C private.
In short, there really isn't much of a difference in how the island has been owned for most of the past century and a half and certainly not for the last decade or so.