Yeah, Most of the country do not recognize Taiwan.
But Taiwanese have their own Passport.
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They have a small army. Having strength of around 130k. If you look at the equipments, it looks pretty decent for a good defense.
https://en.wikipedia.org/wiki/Republic_of_China_Army
A decent navy, An air force close to the size of Pakistan. May be a little bit more advanced if you look at the fighters.
Taiwan, according to China is a break away province, which has it's own Private army, Navy and Air force and have their own missiles and still buying stuffs against China's will, And accidentally fired a Supersonic missile at China recently.
Citizens have democratic rights, can vote, hold elections. People have Individual passports etc... They have embassies, or as they call it Taipei - xyz(country) Economic and Cultural center in many countries. You need a visa to go there and you can't apply for Taiwan visa in Chinese embassy, unless you want to troll the Chinese.