Short answers, pulled from the story.
The Sneakers Game is the nickname for the 1934 NFL Championship Game, played on the 9th of December 1934 at the Polo Grounds in New York City. The New York Giants defeated the Chicago Bears 30-13, denying the Bears an undefeated, untied season.
Beattie Feathers of the Chicago Bears became the first player in NFL history to rush for more than 1,000 yards in a single season, finishing with 1,004 yards in 11 games at an average of 9.9 yards per carry. He shattered the previous league rushing record by nearly 300 yards and also led the league with nine touchdowns.
The Cincinnati Reds were suspended by the NFL mid-season for failing to pay their league dues. Before the suspension, the team had lost its first eight games and been outscored 243-10. The St. Louis Gunners, an independent team, played the final three games of the Reds' schedule.
The Detroit Lions played their first Thanksgiving game in the 1934 NFL season and have played on the holiday every year since. The Lions had relocated from Portsmouth, Ohio before that season and were renamed from the Spartans.
The Ed Thorp Memorial Trophy was established in 1934 as the award for the NFL champion. It was first presented to the New York Giants after their victory in the championship game on the 9th of December 1934, and was awarded through 1967.
Moving the goal posts to the goal line in 1934 succeeded in reducing tied games; no game ended in a tie that season, the first time that had happened since the league's founding. More than 20 games were decided by three points or less. Incomplete passes also no longer resulted in a five-yard penalty.