I’ve referred to it as “The War To End All Wars”, but I can be a sardonic son of a bitch.
You must have an old edition. This is from the latest online edition.
A. Huxley Crome Yellow. There’s the archetypal upper-class British name. 
During WWI, there was some references to the conflict as “War of the Nations” (an encyclopedia yearbook from 1917 I recently read used this). But it’s obvious “World War” and “Great War” were far more cumbersome and won out.
I obviously meant less cumbersome.
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I always found it remarkable that Winston Churchill called the French and Indian War “the first world war”. I don’t know the original source, but the quote is frequently mentioned.
I’ve also seen “The Kaiser’s War” (and for WWII “The Hitlerite War”)
Nine years later I have come across a very interesting quote:
The President of the United States of America, authorized by Act of Congress, July 9, 1918, takes pleasure in presenting the Army Distinguished Service Medal to Mr. Bernard M. Baruch, a United States Civilian, for exceptionally meritorious and distinguished services to the Government of the United States, in a duty of great responsibility during World War I, in the organization and administration of the War Industries Board and in the coordination of allied purchases in the United States. By establishing a broad and comprehensive policy for the supervision and control of the raw materials, manufacturing facilities, and distribution of the products of industry, he stimulated the production of war supplies, coordinated the needs of the military service and the civilian population, and contributed alike to the completeness and speed of the mobilization and equipment of the military forces and the continuity of their supply. War Department, General Orders No. 15 (1921)
As you can see, the order is dated 1921. Unfortunately no reference is given. (It’s from a Wiki article I was reading on Bernard Baruch).
If the citation above can be believed, it is irrefutable proof that the specific phrase “World War I” occurred well before there had been a second World War.
This debate reminds me of “The Great Storm” sketch in The Vicar of Dibley
But how likely is it that a diary entry of a private discussion between two otherwise not very notable officers determined how history would call the war? I think it’s very likely that several people, independently of each other, came up with that term, and that this particular discussion had no effect on common usage.
By the way, there are historians who think that the Seven Years’ War should be called a world war (and then arguably the first one), since it was fought on several continents. But this did not become common usage, and the various theatres of the Seven Years’ War are instead known under separate names, such as the French and Indian War in North America.
A. Huxley Crome Yellow. There’s the archetypal upper-class British name.
Crome Yellow is a book by Aldous Huxley (though granted, just Aldous Huxley is posh enough - understandable, given his ancestry and relatives).