When the cover is shut, the screen turns off. Unless there's some way the proximity sensor is uncovered, there's no way the cover will display what's depicted in the image. Also, the image shows something straight out of an older version of Android (earlier Samsungs). The Moto G has a circular slider.
Suggest you put your money into the original flip cover as the quality is top notch. It's expensive but well worth the price.
You won't be able to view the number etc, of course, but it's a matter of a second to flip the cover open upon an incoming call.