World War I, fought mainly in the trenches along the Western Front from 1914 to 1918, was very much a war between authoritarianism and liberalism.
The first problem is the claim about where WWI was "mainly" fought in the West. WWI was not fought mainly in the trenches along the Western Front. The Eastern Front in the time it was active was about as bloody as the Western Front.
WWI started and finished in the Western Front; the losses Germany took fighting in the East, plus the arrival of fresh American troops, plus the choakhold of the British blockade, is what let allies overrun Germany in the West.
Mainly, to me, means that the other theatres where significantly less important. And that is a strong claim I'd question.
Next, we can actually look at why the various parties entered the War.
Based on records, it appears that the British entered the war based on the principle of the neutrality of Belgium. They had guaranteed its safety for a long time, and where willing to burn the world to keep it neutral; the calculus being the UK wanted the promise of security it provided to prevent the need to fight, you must be willing to fight for nothing but your promise.
There are communications between Germany and the UK where Germany desperately tried to keep the UK out of the war. Germany promised UK the moon, so long as the UK would let Germany walk through Belgium, defeat the French, impose a peace treaty on the French that would involve dismantling their defensive line, then turn and smash Russia.
The UK, at the time, was milquetoast about bleeding to save France, and old enemy/rival. As far as the UK was concerned, if France/Germany/Russia fought each other and bled each other dry a bit, it was fine. Well, they didn't want a single super-power on the continent. But really, if Germany was friendly and France was a bit beat up, that isn't a huge problem for the UK.
Russia was mobilizing to intimdate Austria, the sick man of Europe, over its threats against the Serbs. Russia intended to intimidate Austria into backing down, and if they didn't to bloody its nose.
Austria was still a major power, and some Serb terrorist had just blown up someone more important than the US President is in the USA (the heir to the absolute monarch's throne -- imagine if a terrorist killed the President-elect, and half of the entire Senate and Congress). They where not about to back down over this, and where going to make the Serbian terrorists pay for it. A lot like the USA invading Afghanistan.
Germany had a secret plan to defeat France and Russia, who had allied against them. They did not want to go to war at this point -- based on projections, in another 30 years they would win without having to shoot -- but their plan to defeat Russia and France right now relied on attacking before Russia mobilized. With Russia mobilizing for any reason, Germany had to decide if it was willing to risk defeat. Russia might be mobilizing to give Austria a bloody nose, but once mobilized it might turn its eyes on Germany; and Germany figured it could not defeat a fully mobilized Russia with France at its back.
So for Germany to not risk that, it had to implement its war plan, which was to mobilize extremely rapidly, smash though Belgium, take Paris, force a surrender of the French, then turn around and face Russia. It would be a roll of the dice, but it was plan that plausibly didn't lead to Germany being hemmed in and defeated.
France wasn't willing to let Germany defeat Russia, as it relied on Russia to prevent Germany from defeating France through just repeatedly smashing into France's fortifications.
About the only bit that was a fancy treaty and not a balance of power calculus or victory-in-war strategy was the UK joining the war over the invasion of Belgium.
This is the first spot where Germany has lost the war; they figured they could win against France+Russia, but not against France+Russia+UK. They attack anyhow.
So Germany executes its war plan, smashes through Belgium. Nobody really knows how to fight total war with modern weaponry. Some things go better than expected, some go worse.
Germany treats the Belgish people pretty harshly, which is used in the UK as part of the propoganda in justifying the war. (Germany is pretty authoritarian; I've seen arguments that their harsh treatment of the Belgians was not far misalinged with their harsh treatment of their own people).
The American banks back the Empire/French; the UK mortgages huge pieces of its empire, and the Americans are willing to take it. Now the USA is trading with the UK. It would probably be willing to trade with Germany, but the superior UK navy makes that impossible.
So the UK goes deeper and deeper into debt with the USA. And there is an old saying; if you owe the bank 1000$ you do what the bank says, but if you owe the bank 1,000,000,000$ the bank does what you say.
After the defeat of Russia in the East (Germany smuggles revolutionaries in while bleeding Russia dry at the front; and it works), Germany is still in a losing position. It cannot outlast the Allies; a stalemate leads to failure, as Germany continues to starve.
Either it has to (a) defeat Empire+France in the trenches (and increasing numbers of Imperial troops are arriving, which means that even with the fresh Eastern troops Germany isn't winning the war of numbers), or (b) force one of them out of the war.
The UK is most vulnerable here; if they can cut off shipping UK would starve in months. So they both try to win the surface naval battle (nobody knows if German naval docterine beats UK naval docterine; but the result is stalemate) and open up unrestricted submarine warfare. The second fails to starve the UK (it works initially, then fails) and brings the USA into the war.
The USA joins not only because of the sinking of American ships, or liberty, or whatever, but because the UK's debt is worthless if the UK loses the war.
The Germans then try to break the Empire/France on the battlefield. It almost works, but then it doesn't -- lack of lines of supply and not enough fresh troops doom the German offensive. As fresh American troops arrive, the UK/French/American forces break the German lines, and the war is actually over. Germany surrenders without being occupied; out of food, fuel, ammo and soldiers. Their enemy has solid supplies, fresh troops, and 1000s of constantly improving tanks.
Now, Germany was more authoritarian than the UK and France, and definitely more than the USA. Comparing Russia, Germany and Austria? Not a significant difference.
This is total war. For a side to not lose, it had to mobilize its entire population.
In the liberal western countries -- UK, France, USA -- they had to motivate the population to sacrifice to suppport the war. France used "get the Germans off our land", naked patriotism. The USA/UK/Empire didn't have this -- so they used the authoritarianism of the German and its allied powers as part of the propoganda to recruit support.
The difference was real, but calling it the cause of the war seems wrong. Now, after the war, we had a generation of people who believed they sacrificed almost everything for liberty and freedom; their brothers, fathers, sons and friends died. These people are probably going to consider liberty and freedom to be pretty damn important, and be pissed if politicians discard it as unimportant after the war.
So the very propoganda used to win the war can retroactively change what the war means.
The people in charge are still "that was a good way to manipulate the masses", but the masses are serious about it! They both have political power, and each of these countries now has millions of veterans who are quite capable of picking up a gun and fighting and dying for whatever they believe in. Meanwhile, Russia has fallen to an upper-class slaughtering peasant rebellion.
Democratic Franchise expands in the victorious powers. Those who use the mythology of "we are a nation that believes in liberty" get political wins. And the entire world shifts, just a little bit.