KABUL, Afghanistan — Through the dust kicked up by the pounding hooves of a scrum of horses and riders, a winner emerges. The victorious team gallops around the playing field, holding a flag aloft.

Riders from the Sar-e-Pul and Badakhshan teams enter the field to compete in the final of Afghanistan's annual buzkashi tournament, a traditional equestrian sport in which riders score points using a ...