Officially no, but in practice yes. Whilst it is not a UN member nor does it have much international recognition, it has stuff that make up a country, such as its own passports & laws.
The long and short of why this is the case is because the Taiwanese government was previously in control of the whole of China and got defeated by the communists, where they fled to the island of Taiwan. Despite this, they maintained the claim that they were the rightful owners of the whole of China, with Taiwan's official name still being the Republic of China.
Or in other words, "It's complicated"
