Walter Dürst was a prolific scorer for HC Davos in the Swiss National League A, playing for them through most of the 1950s and up through 1963. In 1959-60 he scored 26 goals and 41 points for Davos in only 14 games, while in 1956-57 he 16 goals and 37 points in 14 games. He played at the 1948 Olympics alongside his brother Hans, where he scored seven goals in five games for Switzerland. Dürst won Swiss titles with HC Davos in 1947-48, 1950, 1958, and 1960 and helped them to Spengler Cup trophies in 1951, 1957, and 1958. He also won three bronze medals at the World Championships (1950-51, 1953), and added four European Championship medals – gold in 1950, silver in 1951, and bronze in 1952-53.