If the world doesn’t want to work with your theories
then change the world
This entire story takes place on the Moon. As such, during construction, every room was built as its own seperate unit that was then placed together. Which would mean that every room can very likely be moved should need be. In other words, this is what happened:
The killer is the butler. He killed the victim, locked the door, set the chain and left through the study window, leaving it open. Then, he remotely moved the bathroom room to the side, and in its place put the study. Thus, the door leading to the bathroom led to the study, while the door to the study led to nowhere. Pretending to go into the bathroom, the butler actually went into the study to close the window. After leaving, he activated the remote mechanism to move the rooms back in their proper order.
My evidence? In the scene where the sargeant throws the key to the protagonist, the protagonist uses the term “snatch” instead of “catch”. If he snatched it, it imples he took an object that was relatively slowly to non-moving - which is consistent to a lower gravity.
i’ll also just change the theory to just plain ol switchable rooms if you only deny the part about the moon