This attraction is called Gyantse Dzong. We arrived at the gates to Gyantse Dzong shortly before opening. For some reason this isn't on the agenda on most tours. The structure is mostly abandoned but is safe to explore if you are careful. My family really enjoyed climbing right up to the very top - with the complete absence of any other tourist for well over 30 minutes.I suspect sooner or later the authorities will not allow tourists to climb all over this like we did. Views from the top are phenomenal l and it was quite a magical experience. There is a small plaque near the top commemorating the Tibetans who refused to surrender to the British (in 1903/1904) and leaped to their death. There is a good explanation in Wikipedia which describes the "British Expedition to Tibet" and the storming of Gyantse Dzong.

The castle is abandoned and used as a museum. The view is nice, but not worth claiming the extra high altitude.