Last week, after a wait of almost a decade, the world’s most popular video game series, Super Mario Bros., finally came to the world’s most popular video game machine: the iPhone. Nintendo’s Super Mario Run went immediately to the top of the App Store charts, above mainstays like Facebook, Snapchat, Instagram and YouTube. According to one estimate, the game was downloaded 37 million times in its first three days.

Unfortunately, despite Nintendo’s history and reputation, Super Mario Run is not a family-friendly game — or at least not one my wife and I will be letting our 6-year-old daughter play. The game is rife with stale, retrograde gender stereotypes — elements that were perhaps expected in 1985, when the first Super Mario Bros. was released in the United States, but that today are just embarrassing.

Super Mario Run begins, as does almost every Super Mario title, with Princess Peach becoming a hostage who must be rescued by Mario. Just before her ritual kidnapping, Peach invites Mario to her castle and pledges to bake him a cake. Upon her rescue, she kisses Mario. The game also includes a second female character, Toadette, whose job is to wave a flag before and after a race, like a character from “Grease.”

By failing to update Super Mario for a contemporary audience, Nintendo is lagging far behind the Walt Disney Co., one of its closest American analogues. Disney’s film “Frozen” subverted and reinvigorated the fairy-tale princess movie; “The Force Awakens” gave us a female Jedi. Super Mario Run doesn’t even try.