Technically Guillaume Apollinaire died during the war, 9 November 1918 according to wikipedia. That's just a nit tho, a little fact I came across looking up these authors, but it got me thinking...

Theres a couple of interesting questions in there though - during the war he sustained wounds he was still suffering from at the time of his death. Did these weaken him in a way that made him more susceptible to the flu? Did the subpar conditions everyone in Paris was dealing with due to the total war (and fronts not too far away) contribute?

In the broad scale - WW1 and the Spansish flu pandemic certainly had effects on each other. Many of the early outbreaks are linked directly to troop movements, and the living conditions in barracks, camps and trenches certainly aided the spread of the flu. Governments were keeping quiet about the potency and spread of the disease for morale reasons. Basically the question of "Is a soldier dying of spanish flu during ww1 a war-related death?" is much deeper than just sorting on proximate cause of death (e.g. flu, or gunshot, etc).

Okay, but in that case many people who died during the war, but not at the front lines, died because of the situation the war had created (lack of food, missing doctors, etc. etc.)

You have to draw the line somewhere. Maybe Apollinaire is a WWI casualty, but not everyone is -- or else it wouldn't mean anything anymore.

Usually also those who die after the war are counted in its casualties, if they died of injuries suffered in the war.

As most towns and villages in Finland, my home town's parish has a "Pro patria" stone tablet at the premises. Naturally most of the men died during 1939-1945, but there's one name who deceased in 1957.

The story is simply that when the tablet was set up in 1980's, his fellow veterans (my father included), who knew his death was due to injuries from war even if it was 13 years after being wounded, decided "Svante deserves to have his name among the fallen" and listed him along.