During the 3 days at Beijing, do I qualify for this 72 hour rule? Or will I need to apply for another one?

Hi,
I am a United States citizen (have US passport, but only single entry visa). I will be in Beijing, but I need to go to Taiwan for a conference for a couple days. I have a round-trip ticket from Beijing to Taipei and back to Beijing. After 3 days from arriving at Beijing, I will be making a one-way trip from Beijing back to Taipei. Therefore, this will not technically be a round-trip flight.

Thank you!