Some very different land rights in Hawaii then in other places in the US. Left over from the Hawaiian Kingdom I imagine. Shades of third world land rights which can be pretty murky at times.
However, it looks like he is trying to end some land easements which are commonly attached to real estate. Easements are what gives people rights to cross other people's real estate so they can access something (often so they can get to their own real estate, or a body of water for example). For example utility companies have easements across nearly everybody's property so they can distribute their products. And no there is no rent or payment. You have to allow access, even to the point of allowing a driveway for example.
Generally, if the easement is still in use, it's nearly impossible to remove. Generally they are permanent. If that easement has been out of use or abandoned over the years, the property owner can try to remove it. All those that could be affected need to be contacted to inform them of that. Sound like that is what is happening, and his lawyers must be assholes about it or something. Sounds like he is trying to buy out the rights, and it's not going well. Maybe many are still in use and people don't want to give them up.
Access rights are very common when the property is large, or if the property is near a lake for example, so since the property is large, there is likely hundreds of old easements. Even more so if most of the surrounding landowners have small properties.
My family has a cottage on a lake in the midwest. There are lots behind us that have access rights to the lake through our property. We and our other lakefront neighbors have been buying up those lots (they were never developed due to the depression, yeah we been there since the 1920's)over the years to remove those access easements. That's probably the easiest way to remove them, buy the property with the rights. So now we have the lot with the cottage on it, and about 4 lots behind it, which is wooded. It makes for a nice quiet place where we won't need to worry about people walking through.
Sometimes people who own property inside national parks are called in-holders, so sometimes easement right owners are called that too. They have easement rights over national park land for access to there real estate. The federal government hardly likes them, and in recent years has put a lot a pressure on some of those property owners.