Hong Kong - Chengdu - Taipei (US Citizen)

Hello,

I am thinking of booking an itinerary that goes from the US --> Hong Kong --> Chengdu --> Taipei --> US. I would only be staying in Chengdu for 3 days (less than 72 hours). Would my stop in Chengdu be covered under the 72 hour free transit policy, as both HKG and Taipei are both considered 3rd regions?

Thank you!