Nintendo’s NES Classic was an immediate sellout, prompting the company to follow up with the Super NES Classic, one of the top-selling consoles in the 2017 holiday shopping season, according to NPD. Nintendo announced on Wednesday that it had sold more than two million NES Classic consoles and more than 2.5 million Super NES Classic consoles in the United States since they were introduced.

For players looking to play the games on a modern device, Nintendo offered 20 classic games to subscribers of its Nintendo Switch Online network, a premium service that went live in September, and has plans to add more.

“People remember the colors and shape of the console and the feel of the controllers from their childhood, and they have a visceral reaction when they first fire up their favorite NES or Super NES games,” said Reginald Fils-Aimé, president and chief operating officer of Nintendo of America.

Sony will follow suit on Monday with the PlayStation Classic, a plug-and-play unit loaded with 20 games for $100. The company has reintroduced older titles over its game network in the past, but this will be an opportunity to relive playing those games on the first PlayStation console, said Eric Lempel, senior vice president of global marketing at PlayStation.

“It’s kind of like watching a classic movie versus a remake or a colorized version,” Mr. Lempel said. “This is the way you remember those games.”

Smaller companies are having success licensing games and repackaging them with new hardware. AtGames, a manufacturer in Taiwan, has sold titles from developers like Activision, Atari and Bandai Namco for more than a decade through its Flashback series, which packages games on replicas of the once popular Atari 2600 and Sega Genesis consoles.