The short answer is. Yes, killing of axis soldiers as well as other forms of punishment toward Germans such as public ridicule, rape, robbery, starvation or dehydration various forms of violence and exposure to the elements were relatively common at the end of WWII.

Troops from the US, UK and various commonwealth territories were occasionally involved in such acts but in far more cases these troops actually saved the Axis prisoners from partisans/mobs, French and Soviet forces.

Probably the two most famous incidences of US troops killing Axis soldiers after surrender are the events following the "Malmedy massacre" and the liberation of Dachau concentration camp.

The "Malmedy massacre" was in fact a series of separate massacres/killings committed by SS troops during the Battle of the Bulge. Estimates differ but somewhere between 360 and and 800 Allied troops and civilians were killed by SS troops In the area around Malmedy during December, 1945. Several US units retaliated by either killing SS troops and paratroopers or refusing to accept the surrender of such troops. There are no official numbers for how many Germans soldiers died as a result. The estimates I've seen range between about 100 and 1,200.

Following the liberation of Dachau in April, 1945 somewhere around 75, mostly Hungarian, Waffen SS troops were killed after surrendering. These men were killed both through direct US soldier action and by US soldiers facilitating their murder by the inmates of Dachau.

I think it's important to remember the scale of WWII there were tens of millions of troops on both sides all across Europe. That means billions of separate interactions between troops concerning surrender. With those kind of numbers it is almost guaranteed that any interaction you can dream up probably actually happened in some form. As a whole the Western Allied troops usually followed international laws when accepting Axis troops surrender. On the Eastern Front, however, massacres of prisoners by both Axis and Allied troops were common.

Allied soldiers taking justice into their own hands was at the very least very common on the Eastern Front among Soviet soldiers. The manner of these executions was usually done "Bottom-Up", meaning they were done by the will and vengeance of the soldiers rather than handed down as a command by high ranking officers. However, the manner of these reprisals taken out by Soviet soldiers became dubious in nature when Stalin at different points in time encouraged Soviet Soldiers to exact their vengeance on the Germans (perhaps as a way to support their activities and keep morale high.) This importantly makes the killings done by the Soviet soldiers sharply different to the organized massacres handed out by German SS officers, for example, which is important not to forget.

Such violence was common nonetheless among all of the combatants, and was usually prompted by emotional trauma of those who dished out the punishment (ex. Soviet soldiers who suffered or lost friends/family under German invasion and occupation in Operation Barbarossa), or by the sharp and disgusted disapproval of soldiers (ex. Allied soldiers exercising their own "justice" as payback for what a German captive(s) might have done, like in the scene you linked. There are instances where Germans were killed by Allied soldiers alike after the liberation of a concentration camp for example. ) German soldiers occasionally did these kinds of punishments as well.

These were overall mostly common on the Eastern Front. The Western Allies received a level of respect from the Germans and were seen as more reasonable, enough to prompt Germans to flee west to be captured by Americans rather than the Soviets. Captured Germans were usually imprisoned in camps, usually in large groups, and spared of being killed. They would be looked at with contempt or made fun of by the guards, but weren't usually outright executed without reason. Instances of Soldiers on the Western fronts exacting these vengeance's occurred but were usually isolated instances. Pillaging and looting was more common among these soldiers, such as in Belgium and the Netherlands.