The question asks why Hemingway included this story in A Moveable Feast. But it is not clear that he did include it! Hemingway died in 1961 before the book was finished; his widow Mary edited his notes into the first edition, published 1964, and in this edition the story does not appear. Whether this was due to Ernest’s intention or Mary’s judgement is now impossible to say. The story appeared in the 2009 ‘restored’ edition, edited by Hemingway’s grandson Seán.
There are some other minor errors in the question:
The title is A Moveable Feast (not The).
The hotel is in Austria (not Switzerland).
It was a man who said that the lecturer ruined Germany (not a woman).
But the major error is the claim that Hemingway did not contextualize the episode. This is the context:
Another year a former German naval officer with a shaven head and scars came to give a lecture with lantern slides on the great and unappreciated German Victory of the Battle of Jutland. The lantern slides showed the movements of the two battle fleets and the naval officer used a billiard cue for a pointer when he pointed out the cowardice of Jellicoe and sometimes he became so angry that his voice broke. The school master was afraid that he would stab the billiard cue through the screen. Afterwards the former naval officer could not quiet himself down and everyone was ill at ease in the Weinstube. Only the public prosecutor and the banker drank with him, and they were at a separate table. Herr Lent, who was a Rhinelander, would not attend the lecture. There was a couple from Vienna who had come for the skiing but who did not want to go to the high mountains and so were leaving for Zurs where, I heard, they were killed in an avalanche. The man said the lecturer was the type of swine who had ruined Germany and in twenty years they would do it again. The woman with him told him to shut up in French and said this is a small place and you never know.
Ernest Hemingway (2009). A Moveable Feast: The Restored Edition. New York: Scribner.
(The story, if it is true, took place in the mid-1920s, when Hemingway spent his winters skiing in the Austrian Alps near Schruns and working on the novel The Sun Also Rises (1926). John Jellicoe had been the British commander at the Battle of Jutland in May 1916. ‘Weinstube’ means ‘wine bar’. Walther Lent was a ski instructor. The Rhineland had been occupied by the Allies in 1918.)
The key point of the story is that Jutland was in no sense a “great German Victory” as claimed by the lecturer. The strategic objective for the British Grand Fleet throughout the war was to keep the German High Seas Fleet confined to the Baltic; the corresponding objective for the Germans was to damage the Grand Fleet so much as to be able to operate freely in the North Sea, break the blockade of Germany, and escape into the Atlantic. Although the Germans inflicted more casualties on the British than they sustained, the outcome of the battle was that the High Seas Fleet turned tail and returned to its ports, ceding control of the North Sea to the British for the remainder of the war. Only the most blinkered and partisan nationalist could describe this result as a “great victory”. The story thus illustrates the belief, among many members of Germany’s armed forces in the years after 1918, in the ‘Dolchstoßlegende’, the idea that the German military had in fact been on the verge of winning the war, but had been prevented from doing so (“stabbed in the back”) by socialists, republicans, communists, and Jews.
The reaction of the Viennese couple seems, with hindsight, eerily prophetic. But the idea was widespread that if things continued as they were, then in a generation or so there would inevitably be another war. For example, following the Treaty of Versailles in 1919, John Maynard Keynes had written:
Economic privation proceeds by easy stages, and so long as men suffer it patiently the outside world cares very little. Physical efficiency and resistance to disease slowly diminish, but life proceeds somehow, until the limit of human endurance is reached at last and counsels of despair and madness stir the sufferers from the lethargy which precedes the crisis. The man shakes himself, and the bonds of custom are loosed. The power of ideas is sovereign, and he listens to whatever instruction of hope, illusion, or revenge is carried to them in the air. […] But who can say how much is endurable, or in what direction men will seek at last to escape from their misfortunes?
John Maynard Keynes (1920). The Economic Consequences of the Peace, pp. 233–5. London: Macmillan.
Similarly, Silvio Gesell:
Trotz des heiligen Versprechens der Völker, den Krieg für alle Zeiten zu ächten, trotz der Rufe der Millionen: »Nie wieder Krieg!«, entgegen all den Hoffnungen auf eine schöne Zukunft, muss ich sagen: wenn das heutige Geldsystem, die Zinswirtschaft, beibehalten wird, so wage ich es, heute zu behaupten, dass es keine 25 Jahre dauern wird, bis wir vor einem neuen, noch furchtbareren Krieg stehen!
Despite the solemn promises of the people that war should be banned for all time; despite the cry of the millions: “No more war!”; against all hope of a brighter future, I must say: if the current monetary system, the economy based on interest, be continued, I dare to assert today that it will be less than twenty-five years until we are faced with a new and more terrible war!
Silvio Gesell (1918). Letter to the editor, Berliner Zeitung am Mittag. My translation.