Typical Chinese solution - a cheap, relatively easy, and dangerous.
These are balistic missiles. The US, and even the Russians, did not develop anti-ship ballistic missiles because their launch and trajectory can easily be mistaken for a nuclear missile launch.
The US Navy SM-3 (RIM-161) is designed to deal with such systems.
If the chinese system can manoever in atmospher its speed is going to be farily low (by rentry vehicle standards) and may be with in the SM-2 engagement envelope.