You obviously didn't pay attention to the story. This game takes place well into the future where there's a group called the Federation who takes over South America after controlling to worlds oil production in the Middle East. ODIN is not an orbital missile launcher. It's just a really heavy rod that uses the rate of gravity to accelerate down to Earth causing a giant shockwave. This is a very plausible defense system as it's dead simple to implement.
Reality check 1: A video game is not meant to mimic real life.
Reality check 2: Yes China has the capability to take on the US in terms of man power. Issue lies in getting all of those men over here, they don't have the equipment to do it.
Reality check 3: This happens in the future and it is very plausible that South America could suddenly become powerful (all they'd need to do is unite and bring in all of the cartels) in said future.
Reality check 4: THIS IS A VIDEO GAME.