It's clear that a lot of work and thought went into this game, so kudos on that!
This concept has potential and is quite interesting - the connection between the physical object and the ethereal one (passing through walls) is something that can really create interesting possibilities. The fact that the link itself is an object that can be effected by some things adds another layer of depth, which is pretty cool. Overall it's quite unique and original!
However, as a game it wasn't fun to play. The floatiness of everything made it feel out of the player's control, and the spike parts are frustrating more than anything else. In addition, if getting the chain cut practically means death, it's quite tedious to have to actually go to some death point in the bottom rather than just immediately dying when falling (Yes, I saw some puzzle required you to reach the stage's end after the chain was cut, but you could still make it insta-death whenever you leave the borders of the level)
As for the theme of the jam - the fact that you have "only one" chain, while technically on line with the theme, isn't really an exciting take on it. In the introduction, Mark said something like "Take something that players expect to had a lot of, and give them only one". In this case, it's a bit hard to imagine how this game would look if you had a lot of chains, so it seems the theme didn't really help in making this game better.
In any case, I think that this game, if the physics would be toned down in favor of more "gamey" controllable interactions, could be quite fun and original.