There's a new piece of software out called Wallpaper engine which allows for cool moving / interactive wallpaper desktops. Its only $3.99 USD
store.steampowered.com/app/431960/Wallpaper_Engine
One of the features is that you can set your desktop as a html5 webpage (which includes exported construct projects).
I can't get keyboard input to work, but mouse inputs work just fine for interacting with your construct projects while its a desktop wallpaper.
Anywhoo, its kinda neat.