no, the qur'an does not specify the charity goes to muslims
i was in sharing a cell for 3 months with a sunni muslim from morocco, he told me that giving to non muslims was also normal because it proves they are superior
obviously they don't give to porn stars and prostitutes lol, and probably not to mormons and jehovas witnesses but probably almost anyone else
the rules in the qur'an also are quite interesting, the requirement for tithing is only 2% (to go to the caliph/imam in your local area) and i don't recall any stipulated percentage for charity giving but it is considered to be buying you more virgins for your mansion in heaven (as is dying for the cause, and converting people)