The DF-21 (CSS-5) has several variants. The DF-21D (CSS-5 Mod 4) is the antishipping variant. It is a garden variety intermediate range ballistic missile (range about 2000 km) that has a non-nuclear warhead that can manevuer to hit a moving target such as an aircraft carrier. How it would do in the face of robust countermeasures is an open question. No one has ever made it work, if the Chinese do it, they will be leaders in this technology.
The U.S. would also have land based assets in Korea, Japan and Taiwan to counter it.