Update Nov 2022: Changed completion date from 1872 to 1873, and added guessed demolition date of 1883 based on Moddsey's notes below.
The date is a guess, based on the year 1872 mentioned in this paragraph from Carl T Smith's "Wanchai: In Search of an Identity":
Marine Lots 29 and 30 were another speculative venture of George Duddell, who bought them at a government land sale in 1849. Augustus Carter, of Messrs Hegan & Co., had bought them at an earlier land sale in 1844, but he allowed them to revert to the government. Duddell sold them in 1854 to Hugh Hamilton Lindsay, of Messrs Lindsay & Co. who disposed of this property in 1861 to Gustav Overbeck and Edward Hutchinson Pollard. They in turn sold it in 1872 to the newly incorporated Hong Kong Pier and Godown Co. The Company overextended itself building godowns and a 1,000 feet wharf, equipiing it with steam cranes, engines, wagons and all the paraphernalia for moving cargo from ship to godown. As principal creditor, the Hong Kong and Shanghai Bank repossessed it in 1873. Four years later the bank found a buyer and conveyed it to Adolph Emil Meyer. In 1891 Messrs Mayer & Co. with other interested parties organised the Wanchai Wharehouse and Storage Co, Ltd. The Kowloon Wharf and Godown Co. leased the property in 1896.
And I'm not sure the exact date it was removed, but it isn't shown on the map in the 1885 Directory & Chronicle, so it was gone by then.
Better guesses welcome!