TOKYO—On their recent honeymoon in Japan, Jason and Nicole Francis savored the temples of the ancient capital of Kyoto and unwound at a resort with a private hot spring. Later they dressed up as a lime-green dinosaur and an Italian plumber and sped through the streets of Tokyo in go-karts.

“I picked Yoshi because I always pick Yoshi in the game,” said Mr. Francis, a 35-year-old emergency-services worker in New Jersey, explaining his decision to don the dinosaur costume.

The game is Mario Kart, a racing challenge from Japan’s Nintendo Co. , introduced a quarter-century ago and now played on videogame consoles globally. A new business here takes advantage of Mario Kart’s popularity and loose regulations on go-karts to offer self-driving tours of Tokyo and other cities, with costumes of characters from the game provided. The company, MariCar, says it books thousands of trips a month and most of the customers are non-Japanese.

It’s part of a tourism boom that is changing the face of the world’s third-largest economy. Many businesses are selling a slice of what foreigners perceive as authentically Japanese. But while visitors are enjoying thrill rides in city streets, plucking off cherry-blossom branches for souvenirs and taking selfies in rented polyester kimonos, some locals are not amused.

“They really are a nuisance,” said Akio Arinaka, a Tokyo-based taxi driver in his 60s, of the costume-clad MariCar riders. “When I see them driving close by it’s scary, especially since they drive in large groups.”