I will say the people who can understand the language at a conversational level is at more than 80%. It is spoken alongside Mandarin in Taiwan, just not as frequently. Many younger people do understand it because they were spoken at home, but when they talk to their peers they speak mandarin.
There are prime time TV shows in Taiwanese language, so that tells you it's spoken widely.
Call the Taiwanese language as a Chinese dialect is debated. See this blog. http://www.tailingua.com/language/ It can be considered as one of the Chinese language family, compare to Latin languages, for example.
When KMT came to govern Taiwan after losing to the Communists, KMT made it mandatory that only Mandarin be taught in schools. It seemed like a good idea at the time because many of the KMT population(commonly known as the mainlanders in Taiwan) came from every corner of China, speaking different dialects and accents. for example... Have you heard of Chiang Kai Shiek or his son talk? I say most of Taiwanese people today can't understand half of their speech.
The majority of population spoke Taiwanese language back then. What KMT didn't consider was keeping Taiwanese language like how the Cantonese was kept in Hong Kong during British rule. Ask the people in their 30's or 40's, students were punished for speaking Taiwanese language in school. YES! punishment for speaking their mother tongue. The older generation will also tell you, Taiwanese language TV shows were allowed no more than 30 minutes a day! One of KMT's authoritarian traits. Of course much of that has been relaxed, speaking Taiwanese is not looked down on anymore. Damage was already done, many young kids grew up not knowing how to speak Taiwanese! sad!
If you've ever been on Taipei MRT, you will hear 3 language announcements... mandarin, taiwanese, english, and maybe a 4th? don't remember.