A hypothetical Somalian king would not answer to a US court, that isn't their main function. These courts exist to deal with issues within the country, which is what I meant by:
I imagine it is actually a lot harder to prosecute people for war crimes in an international court.
They do play a role in international cases though. For example, the US could give legal recommendations to an international court. Whether the person involved is a US citizen or not, the US could get involved if the case related to something within the national interest. They can also give advice on stopping war crimes from occurring, so I find it slightly worrying that this department is being scrapped just as it looks like the US could go balls deep into Syria.
Removing this function of the US government also makes the US weaker on the world stage, because they are going to lose their chance to give input not just in actual war crime cases, but in potential cases too. I suspect that this shakeup relates to this in some way. Allegedly, people are being moved and departments are being switched around for the purpose of getting people out of government.
They refers to countries within the international community and their citizens/leaders.
I'm saying; UN Court on human rights/war crimes > all other 'global' reaching courts (as far as international reputation goes).
Why should a (hypothetical) Somalian King answer to a US court? No, I think we have more reason to hold him to a global court.
Or, we could let regions police themselves.