1) I think that there might be a bug in the command, the duplicates of province/cities in china_map.dta is necessay. If you drop the duplicates, you'll get a incomplete map. Tyr yourself.
2) Use your "score" to replace the "x" in china_map.dta
3) Use option "clbreak" option to control your color like the following:
spmap x using "china_map.dta", ///
id(id) label(label(ename) xcoord(x_coord) ycoord(y_coord) size(*.40)) clbreaks(0,5,11,16,20)
Good luck