Hong Kong Red Cross released a fact sheet on its new headquarters:
The HKRC Headquarters in Admiralty had been in use since 1965. With the rapid expansion of HKRC services in recent years in response to society changes and rising diverse needs, and to match Government’s land use planning for the Admiralty headquarters site, the HKRC Headquarters confirmed to be relocated to Hoi Ting Road, West Kowloon in 2010.[Completion Date: September 2015]
The 3-storey HKRC Headquarters, located in 33 Harcourt Road, Admiralty, commenced operation in 1965, which was the tallest building in the district at that time. In early years, the headquarters of blood donation and the blood bank were on the ground floor, they were relocated to King’s Park Rise, Kowloon later on.
So this building was torn down the make way for new ones. The HQ officially closed an September 11th, 2015. My guess for demolition date is end of 2015.