TOKYO—Athing Mu of the United States won the gold medal in the Olympic women’s 800 meters final on Tuesday, her country’s first victory in the event in more than half a century, as her compatriot Raevyn Rogers grabbed bronze. The absence of South Africa’s double champion Caster Semenya, ruled ineligible due to heightened testosterone levels, opened up the field to a new winner and the 19-year-old Mu took full advantage. She dominated the race, leading almost from the start and crossing the line clear of her rivals in a time of 1:55.21, to secure the United States a second gold in the event after Madeline Manning’s triumph in 1968. Keely Hodgkinson of Britain took silver. Mu, whose parents moved to the United States from Sudan two decades ago, said it was “awesome” that she won gold at such a young age. “I wasn’t really putting gold on that, but as …