Short answers, pulled from the story.
The Chicago Staleys won the 1921 NFL Championship based on a new rule created by the executive committee. This decision gave the championship to Chicago because their second victory over Buffalo counted more than the first matchup.
The decisive rematch occurred on the 4th of December 1921 when a train pulled into Chicago carrying the Buffalo All-Americans. The league applied this tiebreaker immediately in 1921 and kept it until 1933 when they finally abolished it permanently.
No Brunswick-Balke Collender Cup ever arrived at either team's doorstep after the controversy erupted. It is now believed the cup was lost during the administrative chaos surrounding the dispute between Buffalo and Chicago.
The league used an obsolete tradition where multiple meetings meant the later game held greater weight. Frank McNeil insisted the December 4 rematch remained off the record books but the executive committee ruled rematches counted more than first matchups.
The NFL Championship Game turned permanent in 1933 after dividing into Eastern and Western divisions. This standardized schedule also formally abolished the greater weight rule that had favored later games over earlier ones.