I don't think I have an issue with the intent behind the game, but I definitely think that it would benefit from different execution. While the puzzle itself is pretty tedious, I think there's room for games to have a bit of intentional tediousness - those "Sort the Museum/Library/Store/etc." type games have been fairly popular recently, so it's not like that in and of itself is bad. However, I absolutely think that it's in your best interest to make the tedium not tedious, as counter-productive that might sound. Like, I think if the selection and moving stuff was a lot snappier, I could see myself sitting through and moving all the pieces around, even if it took a while. But as it stands now, where I'm also staring down the prospect of going through this process hundreds more times, while there's also time where I just can't do anything for no apparent reason - I just saw the writing on the wall and backed out after about 5 minutes. It's a bit of a shame, too, because the story aspect seemed pretty neat, it sort of reminded me of Yu-Gi-Oh's Millenium Puzzle, and I think exploring that could be very interesting.
For what it's worth, I thought the music was quite nice as well.