Netflix’s “Unfinished Beef,” a live competitive-eating special follows in the plodding footsteps set forth by the annual Nathan’s Hot Dog Eating Contest, the July 4 spectacular on Coney Island. But what it recalled even more vividly were the human-interest freakouts Fox aired around the turn of the century, like “Man vs. Beast” and “Who Wants to Marry a Multi-Millionaire?” Broadcast live on Labor Day from Las Vegas, the competition between pro hot-dog eaters Joey Chestnut and Takeru Kobayashi had more than a whiff of only-in-America decadence and excess.

The special, which ran a little over an hour, built to the 10-minute showdown between Chestnut and Kobayashi, including short, produced packages introducing both parties to the viewer. “I love putting an obscene amount of food in me. It’s what I love doing,” Chestnut told viewers, demonstrating the exercises he performs to keep his jaw strong.

Chestnut and Kobayashi are...