they don't, in any practical sense, and haven't since Chiang died in the 80s, probably even before that.
however, they are threatened with invasion if they ever update their constitution to reflect reality, because that would be taken as "declaring independence".(even though they are completely independent anyway)
Taiwan is independent of China, you've obviously never been there. They still have the old wartime territory definitions in their constitution because updating their constitution would provoke a violent response from China. Nobody, absolutely nobody, takes those claims seriously.