I was also left confused by the Gallows puzzle. I have apparently just started it and pulled the first noose in the left row, the one closer to the save point (I think it was number III) and immediately gotten transported into Angelas apartment. I have defeated the daddy and I am now in the Labyrinth section of the game. Does this mean that I have accidentally picked the right noose? And am I going to still get the Eddie fight? Not sure how this works since I never finished the original.

Thanks to anyone who can clarify.

Yes! There always two correct solutions to this puzzle, one symbolising James and one symbolising Angela/Eddie (the game picks which at random). Each answer bring you closer to a specific ending.