Any person call himself a "Muslim atheist" if he wants to. But definition wise it doesn't make sense.
The author says that the "Muslim" part of the label only refers to his practice and enjoyment of cultural customs. But that doesn't make sense either because (1) the word "Muslim" is directly and exclusively linked to Islam, which is a religion, and (2) every ritual that is decreed in Islam is also religious, not cultural, since the entire Islam itself is a religion. So, any practice or ritual that falls under Islam cannot be regarded as merely a cultural thing. The same goes for labels like "Christian atheist," "Hindu atheist," etc.
The author says that the "Muslim" part of the label only refers to his practice and enjoyment of cultural customs. But that doesn't make sense either because (1) the word "Muslim" is directly and exclusively linked to Islam, which is a religion, and (2) every ritual that is decreed in Islam is also religious, not cultural, since the entire Islam itself is a religion. So, any practice or ritual that falls under Islam cannot be regarded as merely a cultural thing. The same goes for labels like "Christian atheist," "Hindu atheist," etc.