This was the second post office for TST, see Moddsey's notes below. There's a building in about the right position in this 1900's photo, but it's not clear if it's exactly the same one:
It was definitely there in 1910, as it appears in this photo of the first train leaving TST on 1st Oct that year. Here are another couple of views from the 1910's:
Possibly it was built around the same time as the railway terminus, which was just across the road.
From this site the Post Office moved to a larger building across the street, next to the railway terminus.
I'm not sure when the old building was finally demolished. It looks to still have been there in this photo dated 1955:
The present-day Kowloon Park Drive passes over this ground though, so at the latest it would have been demolished when that road was built.