Agreed. There's a lot of frickin' ocean, and they'd have to saturate it, one missile for every 20 sq. miles, in order to have a hope of hitting a carrier. That's assuming the USN ships don't try to shoot down said missiles. They've got a lot of missiles, but not that much. China can talk trash all they want, but there's not much they can do–or would want to do, really.
The fact is, the United States is effectively guaranteeing the trade lanes for everyone. They have not tried to own the oceans for themselves as others did. They have not tried to own resources or markets for themselves the way the Europeans did in the age of mercantilism.
China does what it does out of paranoia. And because people have been jerks to them in the past. But they know that what they have is not effective for waging expansionist war. Those missiles could make it really, really hurt if the United States were to try to take a military action against the Chinese mainland, because that would place a number of CBGs in close proximity to the mainland, where it'd be much easier to track and launch said missiles at them. A more ambitious project would be to cut off American support for Taiwan, and that would be a much longer-term issue for both sides, and one that is not abetted by these islands.
As for the islands, there isn't even any military value in holding them. They are a military liability rather than an asset. Unlike Guam, etc., they are not useful as a staging point, because the range of modern ships makes them kind of useless as a staging or refueling point. They are small–they don't even have fresh water–and thus they are easy to saturate with a few cruise missiles (the USN has 3000 tomahawks in inventory, last I checked?), so, forget about trying to put serious static defenses there. When you look at the fluff, yea, it seems alarming, and that's what it's for. It's politics. The Chinese are doing it because they know the Vietnamese and the Filipinos can't, and the U.S. will just #facepalm and mostly go back to staring at maps of the Middle East the next month, in spite of all the talk of an Asian pivot.