Regrettably, that headline is not accurate. Uighurs are not Chinese, but Turkic.
The people who could be termed actual “Chinese Muslims” are the Hui people, who are ethnically Han Chinese. And the CCP does not seem to bother them too much, or as much as the Sinkiang Uighurs.
The were born inside the statutory limits of CCP China, so legally they are Chinese nationals of Turkic/Uighur descent.
“American” only defines national status. “Chinese” defines both an ethnic status, as well as a national status.
The headline is correct, based upon national status.