The national guard is part of the military, so funded and supported by the feds. Unlike normal army units though, each state or territory has its own national guard unit under the command of the governor. The intention is to give each state the power to quickly respond to emergency situations without needing federal approval. They’re the successors to the old state militias, but have much stronger federal ties now.
The EEA shows up in the list of places it does not apply. They worded it strangely, first calling out the US as a place where it does apply. Then they change it up and say it also applies to anywhere not on this specific list of places