The previous owner of the property erected a gate along their private road, posted "no tresspassing signs", charged for access, and opened/closed the gate at their discretion (leaving it closed for months during winter). I don't have a horse in this race, but that doesn't sound like public access any more than an amusement park is public access.

Yes, it's my understanding that Khosla owns the entire compound and all of the houses. It's one property and was operated as a business by the former owners, the Deeney family.

The previous court case that (SCOTUS declined to hear) was really about whether Khosla needs to apply for a permit for his development work that changes public access to his property. SCOTUS declining to hear the case essentially means that Khosla needs to apply for the permit for these changes -- the implication is that until this happens, the case is not actually ripe for review. If he's unable to obtain the permit, then Khosla may be able to pursue his argument that the state's mandated public access is an unconstitutional "taking" of private property. (IANAL)