Pretty much any GUI framework will have the ability to create a puzzle layout like you describe. Although you probably won't find ready-made puzzle piece components in a GUI toolkit, you can almost always use some kind of canvas and image drawing primitives to draw exactly what you want. I have in the past used Swing to create a GUI that is all custom and doesn't look like a Swing app (see http://free15c.com, the code itself is on GitHub).
It's unlikely that you would need (or want) a full game engine framework. There is more than enough capability in the standard GUI libraries to do this.
Finally, as I mentioned above in a comment, for maximum compatibility with devices of all shapes and sizes, you might consider using an HTML/Javascript implementation. This kind of click-and-drag moving images about would be pretty straightforward.