It absolutely does not. Taiwan was never under any sort of agreement, and the USA has always been ambiguous about its policy towards Taiwan.
This is completely different from the mutual defense agreement that Japan has with the USA, where it has been made very clear that the USA will protect Japan.
I understand you want to have a critical opinion, but you need to look at the facts.
In particular, Japan has the economic and technological might to have been able to make nukes decades ago. They didn't because they received a promise from the US that if anyone nuked them, the US would retaliate with its nukes. In exchange, Japan promised it would not make nukes (and probably also promised to consult with the US on Japanese national security matters). This deal came about because both Japan and the US see the value in keeping the number of countries with nukes low.
