At the top of the design on both covers is a strip of what seems to be some sort of Japanese closet with simple sliding doors. The similarity to such closets is suggested by the panels underneath the image, which seem to be larger doors in front of which the figures are standing: a woman with a lantern, a leaping sphinx, a crouching sphinx, and a woman with a garland.
|Charles Ricketts, design for Oscar Wilde's The Sphinx (1893): front cover
|Charles Ricketts, design for Oscar Wilde's The Sphinx (1893): back cover
A comparison of the back and front cover shows that the doors have knobs on either left or right. It seems that the dove appears when the left door is opened, and the bell when the door on the right is opened. The knob is visible on both sides. The other option - the sliding door has been moved to the left or right - does not explain the changed placement of the door knobs.
Conclusion, for now: there are no Japanese-style sliding doors in front of a row of closets on the cover of Oscar Wilde's The Sphinx. What we see, possibly, are shutters placed in front of the top windows.