This story has been interpreted as a struggle between a young man and his father. This could loosely be seen as a generational war, although a psychoanalytic interpretation is valid as well in the struggle for the son to take the place of the father in the natural progression of successive generations. One thing worth noting is that Georg expects this battle to occur:
A long time ago he had firmly made up his mind to watch closely every least movement so that he should not be surprised by any indirect attack, a pounce from behind or above.
Georg had attempted to put his father into his bed. Georg noted his father's advancing age. Although this seems like genuine concern and care, his father could be taking it as his son trying to rebel and usurp control over his business: a battle based on control and power.
One of the major causes of World War I was the assassination of Archduke Franz Ferdinand of the Austro-Hungarian Empire. (Kafka was born in Prague, then part of this empire.) Ferdinand was killed by a Serbian nationalist. Russia was allies with Serbia and therefore mobilized to defend Serbia, thus becoming enemies with the Austro-Hungarian Empire. Kafka was living in Prague at the time of the assassination. Georg's connection with Russia is worth noting but really seems of little symbolic significance.
This is the historical connection between WWI and the story. However, finding a thematic or contextual connection between WWI and "The Judgment" will be much more of a stretch; but Kafka's style is ripe for multiple interpretations. For example, Georg was the heir to his father's business and Ferdinand was heir to the Austro-Hungarian throne. Each were executed/sacrificed. There is also the connection between Georg (as based loosely on Franz Kafka) and Franz Ferdinand; although this is simply in name, as Kafka and Ferdinand were completely different people with different beliefs, and so on.
A lot of the events leading up to WWI were about different nations attempting to control more land, or reclaim land and power: a battle of nationalism. This could be seen as analogous to the power struggle between Georg and his father, but again this analogy is a stretch. The only other "judgment" that seems to connect the story and the war seems to be a younger generation suffering for/because of/in place of their fathers and forefathers: Georg and the soldiers of the war have been sent to their deaths.
Kafka was disheartened by the war. He also became stuck in Prague because of the war (hence, no chance to visit a place like St. Petersburg). His engagement with his fiance and connection with literary friends outside of Prague were also affected by the war. Given that it was the generation(s) preceding him, Kafka may have rebelled against previous generations (including his father's) for their decisions that led to such a war. This is just another idea about connecting it with the generational struggle in the story.
"The Judgment" leaves much more to different interpretations than just a symbolic connection to the causes of World War I. But if any other educator sees or knows of such a connection, certainly add to this if you can.