The good folks over at XDA have extracted the camera and gallery apps from the new Moto X (2014) and made available for other Android users. You can download the apk, install them on your phone, and enjoy the camera app and gallery app of the new Moto X 2014.
Installation is as simple as downloading the APK and installing it on your handset. If you are running Android 4.4 KitKat on your Android device, Moto X’s Camera and Gallery apps should work without any issues.