Why doesn't the game migrate just like regular windows/phone apps?
According to this
tutorial about how to Migrate Data from an Old Windows Phone to a New Windows Phone: "Keep in mind that this process migrates your accounts, your Windows Phone settings, messages, apps and games. It doesn't migrate the settings of your apps or your saved games. Those are lost and you need to manually configure each app and game on your new Windows Phone.
Also note that nowhere here
(on the WP Machinarium game download page) is saved game state migration mentioned.
Maybe you could try this
WP app called "Transfer my Data"? Hopefully that will serve your current need.