So it's the face that makes it worse?
No, it's not the face. It's the fact that the guard was unconcious and unarmed.
He shot him in the head "just to be sure".
That is what makes it a war crime. How would peple react if, in WWII, the Germans simply shot all Americans instead of taking them prisoner? Since it's war does that mean that anything goes? Can we target hospitals? What if a solder rapes a woman but then kills her. Does that make it OK?
War is not a free for all, no rules.
Do not forget, if you think something is OK for a solder of your contry to do to the enemy, how would you feel if that same enemy did the same thing to one of your solders?
Not everything is black & white but there are some things that are. Not everything is shades of gray.