Again, going by my recollection of the article, there have been attempts to get the legislature to add swimming (and perhaps climbing) to the list but it was blocked by trial lawyer groups.
It shouldn't matter. I don't have the citation handy but the NYS Court of Appeals ruled many years ago that a cliff was an inherently obvious hazard -- that anyone climbing did so at his own risk. I believe the opinion actually had the phrase "like a flashing warning sign" in it. It's been posted here before but if nobody else has it handy I can try to find it again when I get home.
The Mountain House doesn't want their property overrun by climbers, and I assume they don't want the hassle of administering some kind of limited-access system. Better to let a guide service do it for them, I guess. They're well within their rights to ban climbing for whatever reason -- even one that might be so frustrating to climbers as "100 people with backpacks hiking up to Skytop will annoy the carriage-trade hotel guests" -- but the liability thing is and always has been an excuse.