I believe there are two very clear and obvious explanations as to why Taipei is not on the list:
1. English. It is the standard language in Singapore, nearly equal to Cantonese in Hong Kong, and though it is not a Shanghai standard, it is spoken by nearly everyone and regularly in businesses. Here if you speak English exclusively, prepare to look and feel like an a-hole. Without solid Chinese your job growth has a ridiculously low ceiling. So you have to either be a teacher, or get one of the handfuls of crap jobs for nearly the same money as teaching with no real future while you study study study the language. Which leads me to...
2. Wages. They are an embarrassment here. You are expected to go above and beyond the realm of your position, work long hours, and what you make for a white collar job is still laughable by western standards. In many cases, the move to the far east is meant to provide an upgrade to one's standard of living, especially with American wages stagnant. Or it is at least supposed to be a salary match with more job security, since American jobs are disappearing. In Taipei, however, even as a white collar professional, you'll sweating it by the end of the month begging for payday... especially if, god forbid, you had a few nice meals or even (gasp) drinks a couple of times other than Taiwan beer on your sofa. Buying a car? International travel? Large living space? Things of the past.
Of course you can carve out a nice life here if you have minimal needs. But the average white collar professional has higher expectations than the roof over a businessperson's head in Taipei.