Does layover affect my 72-hour Visa free status?

Hello,

I am flying from San Francisco,USA -> Layover in Taiwan but I will not be leaving the airport -> Shanghai (2 days) -> Taiwan -> USA

I thought I can quality because I am technically flying San Francisco -> Shanghai -> Taiwan, but I realized that from San Francisco to Shanghai, I have a layover in Taiwan, but I will not be leaving the airport in Taiwan. Am I still eligible for the 72 hour free visit to Shanghai?

Thank you!