I remember starting my search on the film Full Metal Jacket (which was on SBS last night, it's 2am when I write this so it's valid). I then went to the article on the film Paths of Glory. That took me to an article on a board game called Paths of Glory. That was the most direct route (the indirect involves things like Blackadder Goes Forth and the 1914 Christmas truce and the 1915 football game) The flash game Dog Fight: The Great War sprang to my mind.
Now here is the interesting thing. Beyond flash games like Dog Fight that I linked to above, or Warfare 1917 the gaming world is, as Gamespot says for this review, under-represented in games. Yes, there was in Rise of Nations and Empire Earth II and I'm also assuming other games of that type, have such a concept, but it isn't really the same thing.
I guess it's a little hard to make a WWI game. Although untrue, the popular perception of WWI is summed up nicely in the last episode of Blackadder:
[B]oth sides advanced further during one Christmas piss-up than the next two years of war
In the European theatre this is basically true. WWI was basically long periods of nothing followed by extreme action. I know I'm describing something else (technically the narrative of Mafia is like that, except you only play the action) but I can't remember what it is.
It would be unappealing to play a game like that.
I can already think of one exception. Paul Erich von Lettow-Vorbeck commander of the forces of German East Africa in WWI. His army was the only one of the German colonies to be undefeated. He ran a very fluid campaign, although this was essentially to tie up as many Allied forces as possible, which he did quite well.
You could make a game about that. But I'm guessing that the reason that you don't seem to find one (or that at least I haven't found one) is because a) it's German not Allied, and b) He surrendered peacefully on November 14, after a British magistrate called Hector Croad notified him that the war was over.
As I see it WWI and WWII were a turning point in conventional warfare (like Vietnam was a turning point in unconventional warfare). WWI saw the end to the traditional army. From then on people wouldn't fight on a single battlefield or a series of battlefields with set armies, but saw the "scope" of a battlefield increase exponentially. It also saw the end of traditional tactics, something that many Generals at that time did not seem to comprehend.
WWII saw the rise of very fluid warfare. In a way it was an about face when it came to taking land, but the emphasis turned towards mobility rather then strength alone.
Both wars saw a change in the use of technology and the use of different types of "unit" (I am thinking games here, remember) and tactics to win.
The question is how to translate WWI into a dedicated game. Personally I have no clue what to do for an FPS. I'm sure that you could have a Battlefield-type game, but maps would be limited since jumping out of your trench would most likely equal suicide.
I personally have a bit of an aversion to a total RTS or TBS. I don't really like the idea of having to build proper bases on the battlefield in question ("Hold your fire, I SAID HOLD YOUR FIRE, I need some men so I can build a farm right outside this trench") and I don't really like the idea of taking turns to move people around and fight.
I think that an RTS/TBS (like Aggression: Reign over Europe for example or a Total War game) would probably be the better option. Think about it. You could make your units away from the battlefields (like in real life) and send them there, and have the fighting in real time. Although I still don't know how you would get the fighting done properly. But you would have the advantages of a better overall diplomatic system (something which you would have to implement a "carry over" system for in a total RTS) and a wider variety of things that could be done.
There is one more alternative that I have thought of. Expanding on the "Home City" concept from Age of Empires III. Either have a bunch of cards that you can select to be sent to you, or you could have a "home city" in real time that you could switch to. The added advantage would be that you could ensure that the levels go to specific points of action. I suspect however that this option might be hard to implement without a really, really good system to play it on.
But I'll close with what I have said now, and I'll open the floor to anyone else who has a better clue then I would about why WWI isn't represented as well in games as other wars. Oh, and does anyone know if someone has made a game on the Korean War?