Torriani served as head coach of the Switzerland men's national ice hockey team in 1946–47, and again from 1948–49 to 1951–52. Under his leadership, the national team finished fourth in Group A at the 1947 Ice Hockey World Championships, fifth in Group A at the 1949 World Ice Hockey Championships, third in Group A at the 1950 World Ice Hockey Championships, third in Group A at the 1951 Ice Hockey World Championships, and fifth overall in ice hockey at the 1952 Winter Olympics in Oslo, Norway.