We see Murph finally realised that Cooper is her ghost. Cooper has transmitted the quantum data encoded via manipulating the gravitational waves affecting the watch's seconds hand on Murph's bookshelf. However, the subsequent scene shows that Murph is decoding the watch signal in her NASA office. How?
It seems to be a function of the tesseract. From Ch. 30 of The Science of Interstellar:
By the time Cooper has received the quantum data form TARS, he has mastered this means of communication. In the movie we see him pushing with his fingers on the world tube of the watch's second hand. His pushes produce a backwards-in-time gravitational force, which makes the second-hand twitch in a Morse-encoded pattern that carries the quantum data. The tesseract stores the twitching pattern in the bulk so it repeats over and over again. When forty-year-old Murph returns to her bedroom three decades later, she finds the second hand still twitching, repeating over and over again the encoded quantum data that Cooper has struggled so hard to send her.
(The "bulk" is the higher spatial dimension that exists between the Tesseract's 3D "sides")
Maybe we are thinking too three-dimensionally. It's theorized that some of the higher spacial dimensions are really "small" (though infinite) and curled up and exist within every point of our three-dimensional space. Do not ask me to explain this.
So, maybe the tesseract sends gravity through some of the higher dimensions which are curled up within each point inside the watch, such that removing the watch from the room really doesn't matter because the higher dimensions travel with the watch.
I know "they" are supposed to be fifth dimensional beings, but that doesn't mean the tesseract doesn't operate through higher dimensions.