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In 1904, there was no World Series played between the champions of the two major leagues, the American League (AL) and the National League (NL). The champions were the Boston Americans (now the Boston Red Sox), who repeated their 1903 AL championship, and the NL's New York Giants (now the San Francisco Giants).
1904 World Series Wikipedia
Due to a business rivalry between the two leagues, especially in New York, and to personal animosity between Giants manager John McGraw and American League president Ban Johnson, the Giants declined to meet the champions of the "junior" (or "minor") league. McGraw said his Giants were already the world champions because they were the champions of the "only real major league".
As early as July 5, 1904, as reported in Sporting Life, Giants owner John T. Brush had stated publicly, and in contradiction of a preseason agreement for a championship series between the leagues, that his National League club would not play the winner of the American League "if each wins the pennant in its respective league". At that point in the season, the Giants were comfortably on top of the NL standings, and the New York Highlanders were just 1½ games behind the Boston Americans. The American League race went down to the wire, and the Highlanders temporarily took over first place on October 7 when they defeated Boston. But the Americans won three of their four remaining games to clinch the AL pennant. The Giants, who had won the NL by a wide margin, stuck to and broadened their plan, refusing to play any AL club, either the champion Boston or the crosstown New York team, in the proposed "exhibition" series (as they considered it).
Boston had defeated National League champion Pittsburgh in the 1903 World Series, a contest arranged by the two champion clubs, not by the leagues themselves.
The Giants maintained that the rules for the World Series were haphazardly defined. In the 1903 series, as well as postseason series between the National League and the American Association in the 1880s, the rules for a given season's "World's Championship Series" had been whatever the two participating clubs had agreed upon. The World Series was not a compulsory event and was not governed by an authoritative body, thus the Giants were free to refuse to participate in such an event.
Stung by criticism from fans and writers, Brush in January 1905 drafted rules that both leagues adopted that winter. The rules compelled the two winning clubs to participate and governed the annual determination of sites, dates, ticket prices and division of receipts. These new rules essentially made the World Series the premier annual Major League Baseball event.
Boston slumped in 1905, while New York repeated its NL championship and won the 1905 World Series against the Philadelphia Athletics. The Series has been played every year since except 1994, when a 232-day players' strike ended the season in mid-August.