Alibaba Group Holding Ltd., challenged by Beijing’s yearlong clampdown on private enterprise, is facing another problem: growing competition. For more than 15 years, Alibaba was China’s unassailable e-commerce champion. The company founded by Jack Ma rose to become one of the world’s biggest and most valuable businesses, using hard-knuckle tactics to muscle out challengers. As China’s e-commerce industry has matured, consumers have started to embrace new ways of shopping that favor browsing and interaction over targeted product searches. That trend has left Alibaba playing catch-up in some areas, and competitors have used the shift to gain a foothold in the...