We're essentially talking about an ICBM with a MIRV here. Nothing cosmic (no pun intended). We have existing ABM systems on AEGIS--already pointed out--that are designed to deal with this threat. They may have to be tweaked to deal with something that maneuvers this much (which, at Mach 10, isn't that much), but it's still not that big of a difference.
The big change is that China figured out a way to accurately target a moving object with the warhead, whereas all other ICBM warheads target a non-moving spot on the earth...generally with rough accuracy (you don't need to be THAT accurate with a nuke). It doesn't dramatically change the warhead intercept problem we've already been working on and in large part solved.
“Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.”
― Albert Einstein
Doing the popular thing is not always right. Doing the right thing is not always popular