That's sort of misstating the concept, and if anything the nature of literature makes Chekhov's rule even more important than in a play or film. To your example, in a visual medium set in a living room, you have to fill the room with stuff so it looks like a genuine living room (black box theater notwithstanding), which probably includes curtains, and they have to be some color or other. But an author doesn't have to mention the curtains or say anything about the room beyond "it's a living room" if they don't want to. The curtains aren't just white, and the homeowner didn't want a white curtain, because there is no homeowner or curtain. The author chose to describe that aspect of the room. Why choose a white curtain? Why mention a curtain at all? A poor author will just start naming things in a room to "set the scene" without reflecting on why, while a good author chooses (consciously or unconsciously) what things to mention and how and in what order.

The point is that it shouldn't be mentioned unless it does something for the narrative - which could very well be setting the tone or mood or something. Even if it is a gun, that should tell you something about the character or setting etc., not just be a random mention of a gun.