LAHORE, Pakistan—Pakistan’s first metro, the Orange Line, was meant to be an early triumph in China’s quest to supplant U.S. influence here and redraw the world’s geopolitical map.

Financed and built by Chinese state-run companies, the soon-to-be-finished overhead railway through Lahore is among the first projects in China’s $62 billion plan for Pakistan. Beijing hoped the $2 billion air-conditioned metro, sweeping past crumbling relics of Mughal and British imperial rule, would help make Pakistan a showcase for its global...