All signatories to the Geneva Conventions are responsible for enforcing it. The USA never ratified the Rome Statute of the International Criminal Court and thus has no responsibility to enforce it.
that's the whole thing, the US doesn't agree with that assessment.
People forget, that a war crime is simply a crime that (state) combatants dont have immunity for in war. The geneva convention gives immunity for everything that is not a war crime.
they dont like the specific court, and more generally they dont like when the rule of law applies to them and their allies instead of just enemies. But they do recognize all these things as crime