Rated PG. 101 minutes. At the Chez Artiste

The child chess champions in the irresistible documentary “Brooklyn Castle” don’t take long, as one of these sweetpeas likes to say, to crush you. Year after year, these big brains and little bodies at Intermediate School 318 in the Williamsburg section win chess tournaments, and their winning streak continues on screen. They are a remarkable, funny, inspiring, at times devastating group. Through the eyes of the director Katie Dellamaggiore, you come to know these children, their teachers and parents as you witness their pulse-quickening matches and tears splashed on the family dining-room table. There’s smiling uplift here, but the road is seldom easy and sometimes brutal.

Rochelle Ballantyne dreams of being the first female African-American chess master; Alexis Paredes hopes to be a lawyer or doctor so he can ease the burdens of his immigrant parents. The dreadlocked newcomer, Justus Williams, might be a chess genius; Patrick Johnston, who has attention issues, just wants to raise his ranking. Pobo Efekoro helps his mother with her day care business. He doesn’t mind pushing around a vacuum cleaner for her; she’s trying hard, he says, and, well, his father is dead. By the end of the movie, Pobo is writing a letter to politicians about budget cuts, reminding them of their “moral responsibility” and well on his way from easygoing child to bright light and civic-minded citizen.

“Brooklyn Castle” is partly about the why and how these children became conquerors, but its reach is higher because it looks at pedagogy, politics and their intersection. As Pobo suggests, that means it’s also about moral choices. Providentially for her narrative if not the school, Dellamaggiore — who produced “Brooklyn Castle” with her husband-editor, Nelson Dellamaggiore, and her brother-cinematographer, Brian Schulz — began shooting after the 2008 economic downturn. (Nothing makes for documentary drama like a budget cut that might wipe out the subject of your project.) Bluntly put, to watch a child worry that his school’s marching band and chess program will be cut is to witness the further collapse of a dream far bigger than he is: that of quality public education as a democratic ideal.

The filmmakers open their story gently, though, with mood- and stage-setting scenes mixed in with talking-head interviews. At I.S. 318, “The geeks, they are the athletes,” beams the principal, Fred Rubino, a big man with a broad smile. The chess program was started in 1991 by another principal, Alan Fierstein. By 2006-07, Elizabeth Spiegel, a chess coach and one of the movie’s heroes, was teaching at I.S. 318 full time. (She is ranked an expert.) Pale, reedy, determined, with rotating long and short hairstyles that speak to the multiyear shoot, Spiegel (in the movie, she is Vicary; she has since married), is a paragon of public-school virtue. Another advocate is an assistant principal, John Galvin, who has absorbed the game’s lessons into his teaching philosophy.

The faces of these teachers at times mirror those of their students, who can wear their burdens heavily, with worried eyes and anxious jittering. Being gifted and going from opening move to checkmate in between homework and chores isn’t easy. The children in “Brooklyn Castle” go up against intense pressures: They burn and tremble to win and watching them lose is hard, but they also cope with external burdens like parents and poverty, demanding teachers, uncertain futures and budget woes. They keep going day after week, month after year, urged on by teachers who expect greatness from them and who are rewarded with students whose time before a chessboard brings them trophies, scholarships and cognitive skills. The school is featured in Paul Tough’s new book, “How Children Succeed.”

“Brooklyn Castle” is itself an argument about how children succeed, but it is also unabashedly and somewhat overexcitedly a feature-length mash note to its young subjects. Yet why not? It’s deeply satisfying watching these public school, hard-knock kids win, and Dellamaggiore knows it. They struggle, these children, and their struggling reaches its climax in tournaments that are at once dramatic and nicely cinematic, as illustrated by the many wide shots of rows upon rows of boys and girls hunched over boards in cavernous hotel rooms. Will they win? You know it. Read it and weep: In April, after the documentary wrapped, I.S. 318 became the first middle school team to win the U.S. Chess Federation’s national high school championship.