Very cool concept, although moving the tape feels very tedious. It would probably be helpful if there was a navigation bar that you could click around or something to move around the tape.
I feel it misses the point of the theme somewhat. Although there's multiple reasons you may want to move around the tape, since you're stuck in a linear hallway it ends up being the one and only gameplay mechanic and serve only one purpose; to have the solution for the next door.
It could be a very cool mechanic for a more expanded puzzle game with a more open level design, multiple puzzles to solve, and multiple tapes. Interesting story/mystery would be a must have too.