Willi, son of Wilhelm Köstinger, was an Austrian ski jumper, and Nordic combined and cross-country skier. He competed at the 1964 Innsbruck Winter Olympics in the Nordic combined and finished tenth in the individual event. From 1959-66 he participated in the Four Hills Tournaments as a ski jumper. At the Nordic World Ski Championships in 1966 he was injured in a fall that ended his short career.
During all his years of sporting activities, Köstinger worked full-time as a plumber in his parents’ business in Dorfgastein. He also worked as an official at the 1976 Winter Olympics in his hometown of Innsbruck and took the Olympic Oath on behalf of officials at the opening ceremony. Köstinger moved to Seefeld in the Tyrol in the early 1970s with his family, and ran a hotel.