Cinema history does not want for new waves. But the batch of lo-fi American movies referred to during the past decade as "mumblecore" may be the first example of a no-wave: a movement without movement, a revolution only in the sense of something going round and round with little discernible progress. All of the artists associated with it have moved on to some extent. Andrew Bujalski, the most skilful of the mumblecore group, has made the playful, experimental Computer Chess, released later this month. The prolific Joe Swanberg, whose loosey-goosey methods on early movies such as Hannah Takes the Stairs extended to living with his cast and crew in one apartment during production, directed Hollywood stars Olivia Wilde and Anna Kendrick in Drinking Buddies. And the first lady of mumblecore, writer and actor Greta Gerwig, recently co-wrote and starred in Frances Ha, which married a Nouvelle Vague aesthetic to a mumblecore-style non-plot.

Those directors doubt now whether mumblecore ever really existed. "It doesn't mean anything to me," says Bujalski, whose 2002 film Funny Ha Ha was the first mumblecore work (though the influences stretch back past British movies such as The Low Down and Bronco Bullfrog and into Cassavetes and Rohmer). Swanberg recalls a time when it seemed to be gaining momentum. "In summer 2007 the IFC Centre [in New York] did a mumblecore retrospective and it felt very much like a big deal," he says. "Years later it became crushingly clear to me that few people had heard of mumblecore. It was never a unified movement. There was no manifesto."

That said, there remain identifiable elements to this sub-sub-genre, this footnote to a footnote. Budgets were too small even to qualify as peanuts: Swanberg shot his cheapest film for $3,000, while the Duplass brothers, Mark and Jay, made their festival hit The Puffy Chair for around $15,000. The pool of characters tended to be hipsters and daydreamers; the hero of Aaron Katz's Dance Party USA is hoping to "do absolutely nothing and get the bills paid". There was the casual attitude to sonic intelligibility that gave the films their collective name, and an improvisatory acting style. Not for nothing is there an "um" in the word "mumblecore".

Some found those performances irritating. "I get that they're not actors: boy do I get that!" complained Kevin Kline last year. But it would be a churlish viewer who refused to acknowledge the merit in these roundelays, which hide complex plotting and emotional turmoil beneath apparently shambolic exteriors. Take Funny Ha Ha, shot on 16mm film for $50,000. There is no music, the sound mix is erratic and the credits are handwritten on paper. It takes you a second to realise how cheap the film is, then another second to forget that and become drawn into the romantic imbroglios on screen.

Bujalski has few kind words to spare for mumblecore. "It's never been something I signed on to intentionally," he sighs. "I thought it was silly at the time. If you tell me Swanberg has a new movie out – which he does every 10 minutes, he's a force of nature – then I'd wanna see it because I'm a fan. Tell me there's a new mumblecore movie out and do I wanna go? Probably not."

His protestations are tempered somewhat by embarrassment at having been the first person to utter the m-word within earshot of the media. "I'm the one who accidentally unleashed it," he laughs. The term had been coined in 2005 by Bujalski's sound designer Eric Masunaga. "I made the error of repeating to a journalist what Eric had said. Though I did say that there wasn't a movement, and that even if there was, this would be a ridiculous name for it."

But it stuck, boosted by the sense of a film-making community. There was a you-scratch-my-back casting approach that led to the directors starring in one another's films, or trading cast members. Lynn Shelton appeared in Swanberg's Nights and Weekends, and later cast Mark Duplass in her films Humpday and Your Sister's Sister. Bujalski was in Hannah Takes the Stairs with Gerwig. Swanberg was everywhere. In Katz's Dance Party USA he turns up as a prematurely middle-aged hipster, imposing a "shoes-off" rule indoors and singing the praises of "chair coasters" and side orders: "I feel coleslaw is not something our generation really appreciates as its own thing …"

Swanberg looks back on those years with a qualified fondness. "Hannah was the first film where I had the brainchild that we would all live together. But I did it for long enough that I burned out on it."

Gerwig told me in 2010 that there was no gameplan: "We did them because they were fun," she said. "We had a little money – $20,000, nothing really. We'd get up in the morning, have breakfast together and say, 'What do you wanna shoot today?' It was about shooting hundreds of hours of footage, then putting the most embarrassing stuff in the film. Joe would edit at night, building it as he went. Whatever came up that was interesting would dictate what we filmed next."

Soon the label had become a marketing tool. "We were making small, non-commercial movies without famous people in them," says Swanberg. "And to some extent that word 'mumblecore' became like the famous person in the movie. People didn't know Greta then but maybe they once read an article about mumblecore and that was recognisable to them. The downside was that they could also dismiss the films – if they didn't like one mumblecore film, they'd assume they wouldn't like the others. But whenever 'mumblecore' is used pejoratively now, I'm, like, 'You're kidding, right?' It's an honour to be considered alongside Bujalski – not only does he continue to make amazing films but the films he's already made aren't going anywhere. Film students are gonna be watching them 30 years from now."

Swanberg recently directed several episodes of a new HBO series, Looking, created by Andrew Haigh, the British writer-director of gay indie hit Weekend. The Duplass brothers have edged toward the mainstream with prickly comedies such as Jeff Who Lives at Home, starring Jason Segel, and Cyrus, with Jonah Hill. Shelton has directed episodes of New Girl and Mad Men, and has just shot Laggies, starring Keira Knightley and Chloë Grace Moretz.

But it's Bujalski who has broken away most successfully from his mumblecore past. After two highly paid studio screenwriting gigs, which in his words "came to nothing", he has made his most adventurous film in Computer Chess, a 1980s-set comedy about techno-buffs working on a program that can beat a human at chess. For that authentically flattened videotape texture, Bujalski shot the film in monochrome on tube-cameras from the era. "I've been making movies on 16mm for a decade," he says. "And I've been asked over and over, sometimes with an undertone of anger, 'Why do you still shoot on film?' Some contrarian streak in me made me think: 'OK. You want video so badly? I'll show you video.'" Stylistically, the movie suggests Kubrick on a shoestring. The camera favours gliding, deliberate movements, as though controlled by a chess grandmaster, while the film was shot in the antiquated 4:3 aspect ratio that renders the image square: chessboard square.

The eggheads who populate the film may seem far removed from the procrastinating goofballs littering bars, beds and sofas in the director's earlier work, but Bujalski believes they too are trying to crack the codes of human interaction.

"I came to the subject as a sceptic. My knee-jerk reaction was: what is accomplished by teaching a computer to beat us at chess, apart from taking the fun out of chess? But I realised that it is a very human endeavour. You see the mountain and you have to climb it. And I don't believe you set out to build an artificial intelligence unless, on some level, you're trying to learn something about organic intelligence – about yourself."

His ambivalence toward mumblecore endures. "That word has had a far wider reach than any movie I'll ever make. In an ironic way it's probably the biggest thing I'll ever be a part of. But I make stuff on its own merits. I would be insane if I got out of bed one morning and said: 'I'm gonna make a mumblecore movie.' I wouldn't even know how to."

• Computer Chess opens 22 November. Drinking Buddies is on release now