My thanks to the commenter who suggested "stop imagining"; inputting the word "stop" into the machine resulted in the familiar light beep and the sound of the door opening. A semantic puzzle indeed; it's almost funny, in hindsight. A very simple puzzle, once you look at it in the right manner. I'll keep an eye out for these sorts of things in future.
Upon the opening of the key-bearing cage, I found a sheet of paper; the key was wrapped inside it. Before I inserted it into the door, I looked at the paper; on it was written the following words, in this formatting. It was torn from a lined A4 sheet of paper, as if the writer had been in a great hurry.
"LET ME IN"
Scritch scritch. Heavy breathing; almost feral. The sound of the thing beyond the locked door returned; I hesitated. As if narrated by some cosmic being, a voice rung in my head, as if someone had set the bells ringing. The voice said: Let me in...
I hesitated then, and did not stop. I don't know what to do; I have a key to a locked door, but beyond it lies something that wants to enter. The other door was locked the last time I tried. There's no other ways out.
Imagine a room with no escape...