ICBMs can get up to 4 or 5 miles/sec. An infalling rock from the moon will travel at least 7 miles/sec, correcting what I said before (25 miles/sec). 7 miles/sec is about 25,000 miles/hour.
It all depends on when you launch and how well you can aim.
The kinetic energy of a relative collision at 7/miles sec is enormous. It approches the energy density of a nuclear bomb. Two rocks colliding at that speed would probably be vaporized.
The Chinese economy will never be big enough to pull this off (unless they develop molecular nanotechnology first!).
If your target has a 1 mile-per-second speed advantage on you, and can give itself a nudge during your targeting phase, it'll be out of range before you can react.
The Chinese economy is quite large right now, and is only going to grow if we don't address the problem. The largess will be there to build such a system, if they entrench themselves on the Moon before we can do the same.