The test ship Bi Sheng was seen firing a mysterious unnamed large missile by78 posted in PLAN news and pics
#5,647. This is rumored to be a sea based interceptor. Judging from the proportions of the missile if it is some kind of interceptor missile it is more likely to be a HQ-19 naval equivalent (terminal phase) and not SM-3 (mid-course/ascent phase).
On the other hand I doubt that there will be a SM-3 equivalent in the literal sense as SM-3 is greatly held back by legacy AEGIS systems: namely Mk41 & SPY-1. Personally I think if PLAN was serious about acquiring a sea based mid-course/ascent/boost phase BMD capability, it should just develop its own CG(X) with no compromise on sensor and interceptor.
So basically PLAN version of ASEV? Although they'd probably build a larger ship capable of housing a really large radar and launching HHQ-29, could be good to have a few of these hang around the seas surrounding China.
Depends on what PLAN might want with a dedicated BMD ship really. China isn't really threatened by BMs the way Japan is and she herself is a major nuclear power. Rogue BM threats from nearby can be dealt with by road mobile interceptors and it makes very little sense to develop redundant naval versions of these unless there's some unknown intra-service competition we don't know about.
What PLAN would more likely get are hypersonic interceptors imo. Those will pop up around China a lot more in the coming years and it makes perfect sense to plomp a whole bunch of them on Navy DDGs. HQ-19's info plaque during Zhuhai last year mentions hypersonics defeating capabilities and I suspect the one tested on Bi Sheng is of a similar variety.
To put it simply - The PLAN is facing different operational realities than the USN.
For the PLAN, they are mostly concerned with operations within and around the 2IC (i.e. her front-yard) for the foreseeable future. On the other hand, the USN is operating worldwide, meaning that their warships are often forward deployed farther from their homeland - And often times, within proximity of their adversaries' homelands/front-yards.
In order words - Until China is able to solidify her hold and presence along and around the 2IC, there actually aren't a lot of chances for the PLAN DDGs to mid-course IRBM and ICBM interceptions. And sailing their DDGs off the CONUS's western seaboard in order to be able to intercept ICBMs during the early mid-course phase certainly is a fool's errand, too.
Therefore, partially similar to what
@Cloud_Nine_ has mentioned - Instead of pure ASEV ships that the JMSDF is building right now to defend Japan against missile threats from North Korea and China, the PLAN would better off be procuring successor classes to the 055 DDGs as "true cruisers/CGs" (regardless of whether the PLAN still wants to refer them as DDGs), with greater focus in fleet-wide/region-wide defenses against anti-ship (and perhaps also land-attack) cruise missiles and hypersonic missiles.
TL; DR - The PLAN might as well go with actual CGs that are suited for high-intensity naval conflicts in the "true blue" Pacific, which are balanced in terms of both offense (anti-ship and land-attack with cruise and hypersonic/ballistic missiles) and defense (fleet/region-wide SAMs against the enemy's anti-ship/land-attack cruise and hypersonic/ballistic missiles), rather than having a mobile "offshored-AEGIS Ashore" platform.