The problem is that there isn't exactly any mechanism in punishing those who violated the provisions by using chemical weapons and the invasion of neutral Belgium without warning. If some nations wins a war, these nations wouldn't dare to try their own people for war crimes so it's usually had to be the losers. That said, Article 3 of the 1907 Hague Convention on Land Warfare stated that:

A belligerent party which violates the provisions of the said Regulations shall, if the case demands, be liable to pay compensation. It shall be responsible for all acts committed by persons forming part of its armed forces.

Anyone who signed the conventions must abide by the provisions of the conventions. Violating them was not only morally bad but add more unnecessary suffering to humanity which led to condemnation worldwide. It's like you broke domestic law when you murdered someone for no reason. In World War I, Germany violated the 1907 Hague Convention including the prize rules which stated that merchant ships must not be sunk unless the crew were to be placed on lifeboats before sinking these ships, the invasion of neutral Belgium without warning, and the treatment of the inhabitants in occupied territories. In addition, Germany also initiates the use of chemical weapons against enemy combatants in the battlefield and most major belligerents (including Britain, Canada, France, etc) even did the same thing.

However, there was no such thing as an international tribunal at the time because the concept of war crimes was pretty new at the time when the Hague Conventions of 1899 and 1907 was established. More importantly, any person of a belligerent party who violated the 1899 and 1907 Hague Conventions was expected to be tried by their own nation, not the other.

While signing the Treaty of Versailles, the German government argued that in exchange for paying the damages to the Allied powers, they would try their own nationals responsible for war crimes. The Allied powers reluctantly agreed because they would not foot the bill in occupying Germany so they decided to let the Germans handle their own affairs. This resulted in the Leipzig War Crimes Trials where many German officers, however, were mostly acquitted and/or were sentenced to some months in prison. Many reasons why was because that only German nationals were tried and not the Allied powers. Add to that, some of the cases were carried out alleged on difficult conditions (ridiculous, some of the acts were carried out even under some situations, they didn't have to do that out of watch). The Allied powers

Although largely regarded as a failure at the time, the Leipzig trials were the first attempt to devise a comprehensive system for prosecution of violations of international law. This trend was renewed during the Second World War, as Allied governments decided to try, after the war, defeated Axis leaders for war crimes committed during the war, notably the Nuremberg Trials and International Military Tribunal for the Far East.

Following the end of the Cold War, the same trend led to the establishment of the International Criminal Court in 1998 and went into force in 2002.

Nowadays, any members of the U.S. military who committed war crimes are punished under the Uniform Code of Military Justice (UCMJ).