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Those expecting a documentary focusing on Stieg Larsson’s huge popular “Millennium” series — the high-grade pulp mysteries he wrote as a kind of hobby, and which weren’t published until after his death in 2004 at age 50 — are likely to be disappointed by “The Man Who Played With Fire.” The thing for which Larsson is posthumously world-famous is just barely touched on in Henrik Georgsson’s feature, though clips from the spinoff Swedish and U.S. features are scattered throughout.

Instead, this nonfiction biopic concentrates on something even more compelling: Larsson’s life pursuit of tracking extremist far-right groups as an investigative journalist, a personal obsession that made him an expert in a field that’s only grown more politically relevant since his demise. You don’t get a lot of Lisbeth Salander here. But you do get an overview of fascist/nationalist movements in Sweden and beyond over recent decades,...