Background. Although it was night, there was enough incidental and ambient light for the sniper's face to reflect against the background and to be spotted, hence the need for camo or a mask. The sniper himself was a random German soldier with no other narrative connection to the plot.
The sniper took his first shot wearing his camo 'mask'. The camera looking through the sniper's sights was blurry and indistinct. The music soundtrack at that point became portentous and tragic. He removed the 'mask' for his second and subsequent shots. The camera looking through the sniper's sights was markedly sharp and detailed.
An interpretation of this may be that the sniper knew that his first shot was not lethal, but enough of an injury such that Wardaddy could not use the .50 calibre gun again. He removed the mask for one of three reasons, or a combination thereof...
The first reason is that he did not need the 'mask' any more because Wardaddy was unable to effectively return fire.
The alternate reason, and more philosophical, is that the sniper knew that Wardaddy was mortally wounded and wanted to deliver the lethal round as quickly as possible. Removing his 'mask' allowed him to sight his rifle without the mask's obstruction.
The last alternative is that we, the audience, need assurances that if Wardaddy was to be taken out, it would be by his 'equal', and not some lucky recruit. For this reason, we are allowed to see the sniper's face, which is a grizzled and war-hardened combat vet.
The second reason would go along with the camera effects.
The script, which reveals nothing at all about this scene, is at http://www.imsdb.com/scripts/Fury.html