"Does a club have a duty, a gentleman's obligation not to devalue a neighboring golf course, if possible?"
Patrick;
In America, probably like anywhere else, if some landowner is concerned about a piece of property next to him or in some proximity he's concerned about he better either buy the place or try to create some sort of easement with the landowner not to do something.
NGLA may've had 2-3 or perhaps more opportunities over the years to do something about their contiguous neighbor to the west, Bayberry (Sebonack G.C. now), and they never did.
I'll tell you one of the most notable examples of neighbors doing something deleterious to a neighboring property---it involved Lee Radziwill's house on the ocean in Easthampton one lot to the east of the 15th hole at Maidstone.
For years she had a beautiful unobstructed view to the west down the shoreline and across Maidstone golf course.
Then along comes some mega-buyer and buys the lot between her and Maidstone and constructs a massive wall between his house and her house (so he doesn't have to look at her house) thereby completely blocking her view to the west down the shore and across Maidstone.
Of course she sued him, and I believe the suit went on for years. I have no idea how the lawsuit ended up---all I know is the wall is still there.
The moral of all this is if you want to control something next door to you the best policy is to just buy it.