It's by invitation only, according to
this news article (in Traditional Chinese. Try Google translator, if you don't read Chinese). Amex will start with 100 invitees, selected from existing Amex Platinum Cardmembers in Taiwan.
The targeted invitees are supposed to have more than $200K (NTD$6500K) annual income. Amex chooses Taiwan to be the 4th Asia country to issue Centurion because of spending capacity in those wealthy Taiwanese.
Currently in Asia, Centurion is issued only in HK, Japan, and Singapore.