The jì reading is classical / literary and survives mainly in Tang-Song poetry and historical prose, where
骑 names a horse-with-rider as a counted unit (one jì = one mounted soldier). Modern Mandarin has largely collapsed both readings into qí — Du Mu's
一骑红尘 is the classroom example where teachers still insist on jì, but most mainland speakers now read it qí. Taiwan dictionaries preserve jì more strictly.