This editor was originally posted in the old Forum, and there's a number of things I didn't bring over to this post; I thought there would have been no need for all that stuff. I should have left at least the basic instructions on how to install it.
I kind of figured that you didn't have KS installed, but made a more generic reply just in case it weren't the case. Of course, technically speaking, you'd only need the Data folder, because it contains all the tilesets, music, etc. that the editor needs to use, as well as the Template.bin file, which is actually a .knytt.bin file for the basic level that is opened whenever you create a new level.