Rather shallow I would instead say.
And, well, they have future tech and super robots, which might make controlling such a large territory possible.
Also everything that isn't the 'murricas and Japan is recently occupied territory. It's never stated how well they really controll it (and the real point for the war was getting magic caves anyway).
If anything needs proper explanation, it's fucking Ching Chong Ping Pong.
Still, CG is FAR from the worst, I wouldn't even call it "bad". It's just, as I said, somewhat shallow, but a lot of things can be handwaved by their better tech.
If you want something stupid, then look no further than South Africa conquering half of the world - with normal tech!