How significant was The Battle of the River Plate in terms of World War Two?
The survival of Great Britain depended upon her merchants shipping. In World War I the Germans came close to starving England through the use of their submarines sinking British merchant shipping.
In preparation for World War II the Germans developed a new type of ship, heavily armored, fast and with the ability to stay at sea for a long time. Three such ships were built: Admiral Graf Spee, Admiral Scheer and the Deutchland (renamed the "Lutzow.")
Basically these ships were to be the "Fox in the henhouse." The "henhouse" being British transports. The idea was to sink a British merchant ship, and then quickly disappear to some other part of the Ocean. This would force the British to use MANY ships, of an important size, to search for these "Pocket Battleships." This would weaken the British navy. Frankly the British were very worried about these ships.
The Graf Spee was able to sink nine, having a total of 50,089 tons. In that short space of time they were far ahead of even the "Wolfpacks."
The sinking of the Graf Spee was a great moral builder for the British. They had severely damaged a major threat to their supply line using three Cruisers, only one of which should have had any chance of fighting such a powerful German ship. While militarily it was important to England, it was a great blow to German moral. All that money, manpower and effort had been lost in the first three months of the war. It was a bad beginning for the German Navy. It caused some doubt as to the value of a surface Navy. For the English it was confirmation of their faith in the superiority of their sailors and ships. Very important in view of the fact that in the first three months of the war the British had little to brag about.
So I would say that while militarily it was important, it was even more important on the level of moral.
Hope this helps, John