The Chinese Anti-ship ballistic missiles (AShBM) are veery different beasts. First of all, they have a different trajectory that is more difficult to intercept, so that they can maintain lower altitudes.
These lower altitudes allows the ballistic missile to maneuver. This makes their trajectory unpredictable, which makes missiles like the SM3 almost useless.
In combination with this, China also has hypersonic glide vehicles, which are not only harder to target, but also fly on non-ballistic, fully unpredictable trajectories at such altitudes that the horizon becomes a real issue.
To top it all off, China and Russia are both in the advanced stages of construction (Russia is farther ahead and should Comission them soon) hypersonic cruise missiles, with possible sea-skimming terminal modes.
All in all, the SM3 missile is pretty much useless against that threat.
The better explanation is that this is a test that congress asked for, and that if anything is more suitable to target North Korea, not that it's very likely it would be perfectly effective against North Korea as they have second-stroke capability and sure as hell won't send a single missile with a single warhead, more like 15 real missiles with a mix of decoys and nukes plus multiple dummy missiles with no real payload. But it's a start against a North Korea class threat.
Anyways, here's a lesson from modern warfare, never rely on countermeasures.