That's because Rankin never played pro hockey. He starred in his hometown of Stratford, Ontario and later in Toronto from 1904 through 1914. The NHL wasn't even officially formed until 1917.
Rankin, who was from a family full of hockey stars, was a junior hockey sensation in Stratford. A brilliant skater and stickhandler, Rankin, one of the best rovers of all time, moved on to Toronto where he led the Eatons to back to back provincial senior titles in 1911 and 1912. He later moved to St. Michael's, falling in the finals in 1913 and 1914.
In a region that also boasted Frank Foyston, Harry Meeking and Alf Skinner, Rankin was an all star rover each of those seasons, always challenging for the goal scoring championship. He led in 1911 and 1913 (when he scored 22 goals in just 5 contests). In total he scored 63 goals in 21 games over those 4 seasons, plus another 15 in 13 playoff games.
His greatness was renowned, and the pro teams wanted him. He reportedly turned down $2,500 for one season, which was a significant amount of money at the time. Teams from Ottawa and Toronto both offered big money, but he steadfastly refused to give up his amateur status, mostly because he did not want to give up his regular job (his occupation remains a mystery to me at this time).
Rankin's career was cut short by World War I as he joined the Canadian Armed Forces.
Though he never returned to the ice as a competitive player, he did step behind the bench. He coached the Toronto Granites to the gold medal at the very first Winter Olympics in Chamonix, France in 1924.
Rankin died in 1932, making his inclusion in the Hall of Fame in 1961 a posthumous affair. Even if he had still been alive he would have been greatly overshadowed on his induction night. His induction class included Rocket Richard, Syl Apps, Milt Schmidt, Charlie Conacher and George Hainsworth.