“Queen of Katwe” doesn’t veer from the family-friendly inspirational sports movie playbook — there’s a plucky protagonist looking for a way out, a hardworking single mom concerned about false hopes, a committed coach seeking personal redemption. But the Disney release from veteran helmer Mira Nair is quietly radical in enough ways to make you cheer despite the cliches.

In telling the true story of a preteen girl in Uganda who becomes an unlikely chess prodigy, “Katwe” is the rare Hollywood film that never sets foot in the U.S. and doesn’t focus on a white hero to make that point of view more “universal.” It respects its characters’ Christian faith, without emphasizing religion in an attempt to rope in “faith-based” ticket buyers. And it’s a film about real people facing real problems, not pre-sold brands battling it out amid CGI-enhanced spectacle.

What that means for the box office is hard to predict — the film could land anywhere from well-intentioned disappointment to sleeper success in the crowded fall season — but it should emerge as a valuable addition to Disney’s library once word of mouth spreads among family audiences and educators.

When we first see heroine Phiona Mutesi (Madina Nalwanga) she’s on the cusp of becoming a national chess champion, and the narrative skips back a few years to trace how she got there. Only 9 years old when she discovers the game, Phiona lives in extreme poverty in a shantytown called Katwe, just outside the capital city of Kampala. Her mother Harriet (Lupita Nyong’o) hawks vegetables to support Phiona and her two younger brothers. Another sibling and Phiona’s father have both passed away, while teenage sister Night (Taryn “Kay” Kyaze) has taken up with an older man.

Bleak circumstances aside — and the script by William Wheeler understandably omits many of the harsher details of life in Uganda included in Tim Crothers’ nonfiction book of the same name — Phiona is nothing if not determined. She refuses to let her gender, social status, or lack of an education (her mother can’t afford the expense of sending her to school) stand in the way of mastering the strategies of chess.

Still, she wouldn’t get very far without the help of Robert Katende (David Oyelowo), the missionary and former soccer player who starts up a chess club in an abandoned church. Robert’s devotion to giving children a foundation to improve their lives is rooted in his own painful experience of being orphaned at a young age. Instantly recognizing Phiona’s natural skill, he mentors her through a series of increasingly far-flung competitions.

Robert also finds himself repeatedly at odds with Harriet, who initially finds his interest in Phiona too good to be true and then begins to worry that the more her daughter sees of the world, the less satisfied she’ll be living in Katwe. While those narrative beats are generally familiar and almost wholly predictable, it’s to the film’s credit that the drama revolves entirely around family dynamics and sociological circumstances — there’s no artificially manufactured rivalry or unnecessary romantic subplot to clutter things up.

After a few recent stumbles (“The Reluctant Fundamentalist,” “Amelia”), Nair finds herself back on firmer ground and makes a good fit with the engaging material. “Katwe” may lack the nuance of films like “Monsoon Wedding” and “The Namesake,” but it nevertheless benefits from Nair’s eye for cultural specificity (she’s had a home in Kampala for more than two decades) while retaining a buoyant touch that befits the story’s all-ages appeal.

Indeed this is both a sunnier and more lived-in domestic vision of Africa than U.S. auds are accustomed to (an admittedly small sample considering the handful of Hollywood films that even bother to visit the continent), and the top-notch craft contributions bolster the allure. From Steve McQueen’s regular cinematographer Sean Bobbitt to Spike Lee’s editor Barry Alexander Brown and “The Last King of Scotland” composer Alex Heffes, Nair has assembled a distinguished crew that doesn’t play down to the film’s PG rating.

But the film’s strongest assets are undoubtedly its actors. Nalwanga is a natural, and if she’s a bit too mature to credibly play Phiona in the film’s earliest scenes, the authenticity and spirit she brings to her character’s empowering journey mitigate any quibbles. Oyelowo further establishes himself as one of today’s finest leading men, bringing deep emotional reserves, an innate sense of goodness, and a playful side that earn Robert a memorable place in the substantial canon of onscreen coaches.

Rounding out the principal trio, Nyong’o is simply radiant in her first live action role since winning an Oscar for “12 Years a Slave.” She imbues what could have been a stock mother figure with such inner fire that Harriet feels worthy of a movie all her own. And the most exciting thing about seeing a film like “Queen of Katwe” come out of a major Hollywood studio is that that idea suddenly seems a little more possible.