When employees at fashion giant Shein crowded into an elevator in the company’s Guangzhou office at the end of one workday this summer, no one took notice of Sky Xu. The quiet man in the corner was one of the wealthiest people in China, the driving force behind an app that has quickly become one of the top shopping destinations in the world—and the boss of everyone riding the elevator. With Xu that day was Frances Townsend, a senior adviser to Shein. When they left the building, she said to him she was amazed that the workers didn’t seem to...