You could just copy the files over and then set that as the boot partition
Ah yes, now its making sense somewhat. That clone disk feature is specifically for hard drive upgrade, so its going to copy the whole disk. You need to make a new backup instead, which well give you a page where you can select whole disks or just individual partitions. You would than take this backup and restore to the other disk.
I've got Acronis 10 so things look different but looks like other than a few extras the newest version does the same thing. If you can't find the right option I'd recommend booting from the bootable media instead. Well probably be a lot easier to locate the backup button when you don't have all those little OS extra features on the screen.
And if you want to do it from Windows you're on the wrong page it looks like. You need to click on "Backup" on the left hand side.