The position of the marker is approximate. The descriptions in the articles below say it was at "the junction of Wyndham Street and Glenealy", but I'm not sure exactly which building that was. Location confirmed to be 29 Wyndham Street, see the comments below.
A search for Wyndham Hotel in the old newspapers turns up a couple of hits. First from The Hong Kong Telegraph, 1924-3-11 page 1:
To be pulled down.
Site for Chinese flats.
The Wyndham Hotel, situated at the head of the street bearing the same name, is to come down. Residents have received notice to vacate their rooms at the end of the present month, when the work of demolition will commence.
This hotel is one of the many premises of which notice of demolition was given prior to the framing of the new legislation which aims to retain those buildings that are in a structurally sound condition. For many years it has been a popular place of residence, and has filled a great need in providing conveniently situated and comfortable accommodation at a very moderate price.
As a result of the decision to pull the building down, some 30 guests, many of whom have been at the Wyndham for a considerable period, are compelled to seek new quarters.
Plans for the erection of a block of Chinese flats on the site have been approved.
The demolition of this hotel will mean the removal of a very old landmark from Hong Kong. Many years ago it housed, for a considerable period, the Hongkong Daily Press, but later was acquired for the purposes of a hotel.
Second from The China mail, 1924-4-22, page 5:
Wyndham Hotel accident.
Workmen's apprentice injured.
At 2.40 this afternoon, part of the Wyndham Hotel which stands at the junction of Wyndham Street and Glenealy and is in the course of being demolished, collapsed with a resounding crash. Debris was thrown across the street to the Dairy Farm's offices and passers-by had narrow escapes. From a foreman who is in charge of the work of pulling the hotel down it was gathered that all the fokis managed to get out from the building before anything serious happened but a Chinese boy who had the appearance of an apprentice and was working at the place was taken away by other workmen. He was bleeding in several places but could walk with support.
A mound of old bricks etc, was lying outside what used to be the entrance to the old hotel. Passage outside was blocked for some minutes.
A search in HKGRO shows it is mentioned in the Jurors Lists for most years between 1911 and 1924 (and again in 1927, but I'm not sure why!). That fits with the descriptions above, that the hotel provided local residents with long term accommodation. I don't know if they also took in tourists as short-term guests.
Any other information about the Wyndham Hotel gratefully received!
Noticed an advertisement for the Wyndham Hotel in 1913 giving the address as 29 Wyndham (Flower) Street.
re: Wyndham Hotel
Thanks Moddsey, I've moved the marker to number 29. (To make sure the road hasn't been renumbered since then I checked an 1897 map and it showed number 29 at the same location it is today.)