Joef,
You can't simply "install" applications from a backup. You can mount your image on the second computer, browse it, find your data files and then copy them to the second computer, but you can't simply "copy" over your applications like that.
If you want to take the complete image and "restore" it to the second machine, you can however do that. This is called an HIR (Hardware Independent Recovery). You are basically taking an image from one computer and restoring it to a second computer which has completely different hardware. If you decide on this route, definitely read the ShadowProtect manual regarding this procedure before you attempt it.