[fiftymegaton]

Even if the Chinese have laser weapons I doubt very much that they could hit a target traveling at 13000 mph with it. At least not for a couple decades(I would think).

[BenLurkin]

Except the shuttle has to re-enter along a very narrowly defined path. Assuming they had the mega-watts (or whatever it would take) they could throw the beam into the path and wait for the target to fly into it.

For all that matter, any space faring power could strew debris along the re-entry path and hope for lucky shot.

[Dead Dog]

The Russians tracked and hit a shuttle with a megawatt laser in the 80's. It disabled comm and caused some discomfort in the crew. The technology is not that sophisticated, armature astronomers track satellites every day (night).