The blank space at the bottom of the image on the left (and at the top of the image on the right) is for the chemically treated patch which ignites the matches when stuck. So this cover is either a printer's proof of the proposed design, or it has been removed from a batch in the process of being manufactured.
It probably dates from some time between 1913, when the baths opened, and 1920, when bookmatch covers first included the safety warning 'close cover before striking'.
Bryant & May—in the 19th century an actual company rather than, as today, merely a trademark—was a major producer of matches. They also opened an Australian factory in Melbourne in 1910. The cover of the bookmatches they made for the Australia Hotel Turkish Baths in Sydney already has its striking pad, and its matches have been used.
© Malcolm Shifrin, 1991-2023