Rösti was a member of the Swiss national ski team at the beginning of the 1970s and specialized in the giant slalom and slalom disciplines. A first place in a World Cup race in the points he achieved on January 5, 1970 as tenth on the difficult slope at Chuenisbärgli in Adelboden. Two years later he came on the podium for the first time with a second place in the same place. He missed his victorious team-mate Werner Mattle by five hundredths of a second. With this success behind him, he traveled to the Winter Olympics in Sapporo. In his favorite giant slalom discipline, he was the best Swiss in 7th place after the first round, but was eliminated in the second round. In the slalom competition that took place three days later, he finished 15th.
The post-Olympic World Cup season then turned out to be his most successful. At the end of the season there were three places on the podium and a fourth place and Rösti was third in the discipline ranking of the World Cup for the giant slalom behind Hansi Hinterseer from Austria and Erik Håker from Norway. In the same year he won his only Swiss championship title in giant slalom .