Presuming he regards Taiwanese as a distinct language in its own right, then no. It should be:
teaching the Taiwanese language
However, it's possible he doesn't mean that. He might be using 'language' in a completely different, uncountable, sense, in which case it's correct.
What do you think he means?
I don’t think he regards Taiwanese as a distinct language in its own right.
The following is what I think and what I've found.
Chuang isn’t the author of the book(
Google Books, first sentence/paragraph). He wrote the foreword(“Recommendation”) for the book. From the sentence in #1 it’s not clear what he means, but after reading his writing and part of the book(*1), I can confidently say that he means “teaching Taiwanese, the language, not the people,” much the same way in these examples:
“…, indicating a shift in emphasis from
teaching Taiwanese language to Western missionaries to training Chinese-reading Mandarin speakers.”
— Taiwan: National Identity and Democratization By Alan M. Wachman 2016
“Unfortunately, most Taiwanese websites are limited to
teaching Taiwanese language or the culture of Taiwan.” —
Culture Shock—Taiwan By Dr. Georg Woodman 2010
(*1) The book is mostly written in Chinese, with the help of IPA symbols and alphabets to make up for the sounds, and some words, not present in Chinese characters. For non-Minnan/non-Taiwanese Chinese speakers, I believe they can still make (some) sense of this book. Nowhere in the book mentions that Taiwanese is presented as a distinct language in its own right. It's still Chinese, which Taiwanese is a part or a variety of.
