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As Moddsey guessed, this was built where the Metropole Building stands today. The site was bigger then, stretching from King's Road (then the seafront) back to today's Ming Yuen mansions on Peacock Rd.
I'm not sure the exact dates it was built / demolished, but it appears in the newspapers from 1899 til 1906, when the site was sold. I'll put those dates in as a first estimate.
The notice of the sale gives the lot as IL 1705, which fortunately can still be found on map.gov.hk.