Sure, there are other sports with games on Thursday—but NFL matchups are all that matters
Thanksgiving and football are inseparable. Ever since we Americans began to gather each year and give thanks with our families, we've looked for ways to avoid having to talk to anybody at the feast. Nothing has helped distract us from our relatives more than watching 22 young men bash skulls for several hours.
No, the Pilgrims didn't play football at their first dinner. There was no two-hand touch, "five-Mississippi" game in 1620. The Pilgrims didn't go much for sports. They hunted, but it was less for recreation's sake than to avoid dying.
But the Pilgrims also didn't hold the first Thanksgiving. Not really, really anyway. Like so much of the lore around the Plymouth colonists, the meaning and iconography of the modern holiday was sort of retroactively layered on by national myth-makers starting in the mid 1800s. President Lincoln, casting about for symbols to unite the nation during the Civil War—there is absolutely no truth to the rumor that he was secretly working for Hallmark—formally proclaimed the last Thursday of November a holiday in 1863. The first game of intercollegiate football—which probably looked more like rugby—was November of 1869, and the newly formed American Intercollegiate Football Association staged their first championship game on Thanksgiving in 1876.
By the 1890s, it was a craze. Thousands of high school, college, and semi-pro teams held their championship match on the holiday. These games often became known as "Turkey Bowls," but they should not be confused with "Turkey Bowling"—a sport developed much later that isn't as popular as football, mostly because the birds tend to get stuck in the automatic ball-return machine.