Changing Airlines Seoul to Chengdu to Taipei

Greetings. I plan to visit a friend in China using my award points on one airline. I plan to directly book a flight from Seoul to Chengdu then leave within 72 hours on a different airline carrier to Taiwan. Though the airlines aren't the same and the tickets are one way (but allow a 72 hour window between flights), do I qualify for the 72 hour visa free entry?