If it did, the ICC is not a higher court - it's not in a judicial hierarchy. It's an independent agency created to prosecute war crimes and similar behavior. (The following is my impressions; hopefully someone knows the specifics.)
If a dictatorial government leader commits war crimes, who prosecutes them and under what law? Unless they lose the war, the victims can't prosecute. Unless they lose power, their own country won't (and even if they do, they often walk away free). Third party countries have little motive or standing - there was no crime commited in their jurisdiction (though universal jurisdiction now addresses that to some degree). The tyrants could commit horrors with impunity.
The ICC presents some real deterrence: Maybe you can get away with the war crimes today, but someone is watching and may arrest and prosecute you later. Maybe it's better to fight the war sufficiently adhering to international law on warfare (e.g., the Geneva Conventions), and avoid that risk.
Copyright infringement is not included.
https://www.ohchr.org/en/instruments-mechanisms/instruments/...