The link to the pictures that you posted isn't working so I did a search for an abandoned island in New York.
Are you talking about North Brother Island, near the Bronx? I saw the photos, and to me the creepiest one is the rusty examination table from the old morgue. The place does have a dark history because of it being a leper colony, and because Typhoid Mary lived there for 30 years, and because it was a forced drug rehab place for juvenile delinquents, but you would think that they could do something with that piece of land besides have armed Coast Guard guys protecting it.
People who believe in paranormal stuff would probably say it's haunted because of the ship that crashed there and killed 1,000+ people, and the fact that all kinds of people died there of various medical problems.