For the same reasons that the US approved mergers of European and sometimes Chinese companies. If they have fairly major operations in China then China can get involved.
I'm not sure if either AMD or Xilinx has sufficient operations in China to justify it, though.
"The companies had been waiting nearly two years for their deal to clear global regulatory hurdles. The takeover had been approved in eight other jurisdictions, including the European Union and South Korea, since it was announced in October 2016. China was the lone holdout. "
