The area surrounding the summit of Mount Saint Helena is (according to GaiaGPS private lands layer) owned by Montesol Ranch LLC. If you search the web for this, you’ll see it is the largest private land owner in the Napa area, and you’ll find multiple articles about work to convert and protect the land as a public park. The sign informs you that you are leaving Robert Louis Stevenson State Park, and access is granted by the private landowner (who can choose to revoke access, should they choose). It also lets you know that the State Park is not in charge of maintaining that area.
It is allowed for you to hike up there, but be respectful of the fact that this is private property and as with all hikes, practice the principles of Leave No Trace.