The erudition of the discourse is electrifying: two towering American intellectuals of the riven 1960s at one another like fighting cocks on primetime TV – Gore Vidal and William F Buckley Jr.

They are compelling – to the point that Best of Enemies, a documentary about a remarkable series of debates between these two on ABC television in 1968, is the surprise but deserved success of this summer’s movie festivals in the US.

Why, though, would a film reviving debates between upper-class intellectuals half a century ago make for a hit film in 2015? “It took a long time to make, because no one wanted to fund it,” explains vindicated co-director Robert Gordon. “People thought: ‘Who’ll want to watch a movie about a couple of public intellectuals arguing on TV?’ Well, we made the movie, and they were wrong.”

The success is partly due to the unimaginability, nowadays, of such cerebral prizefighting before a mass audience. The setting is America in the mire of Vietnam: Buckley and the right digging in to fight a patriotic just war on communism and what they saw as decay at home; Vidal and the radical counterculture in ferment against both the war and the society waging it.

Vidal and Buckley argue with visceral sincerity across that fault line, in a way that the routine polemic of today lacks or plasters over. “Nowadays,” says Gordon, “you could watch the shouting matches with the TV switched to mute. You know what they’re going to say; it’s all noise between the commercial breaks.”

The debates were staged as a high-risk strategy, as ABC fell behind rivals. Buckley founded and edited National Review, credited with having inspired Ronald Reagan; Vidal was a homosexual historian and novelist from a Democrat family.

Their intellectual dispute was one of informed, passionate loathing. As the late Christopher Hitchens, a close friend of Vidal’s, says in the film: “there is nothing feigned about their mutual antagonism. They really did despise each other, it comes from a deep well.”

Their rivalry fell within a deep well of historical tradition: Plato versus Aristotle pitting idealism against methodology; Jung versus Freud over the unconscious; Vavilov versus Lysenko over genetics and the environment. Or Albert Camus and Jean-Paul Sartre, existentialist friends who fell out over French Algeria and the politics of the individual against those of the masses.

All of which, notes Gordon, stands in marked contrast to the chumminess between Bill Clinton and George W Bush, after decades of professed disagreement, “unless of course that is just appearance too. When the cameras went off Buckley and Vidal, these guys didn’t go for a drink”.

Memphis-based Gordon speaks as both a producer-director of this film and author of a wonderful biography of blues master Muddy Waters, Can’t Be Satisfied, and thus addresses his theme as lying – like Muddy’s blues – at the kernel of American culture. And this at a time when there were “bad lines being drawn” – as the musician Stephen Stills put it – which cogently inform the present and across which there could be no compromise.

At one level the argument is universal, as Richard Wald, then vice-president of ABC News puts it: “What kind of people we should be, who is the better person?” On another, the soul of America is at issue: “The stakes were the republic itself,” says Gordon. “They both believed that were the other’s view to prevail, it would take down the republic. This was not just dislike or even hatred, it was also fear – fear for America.”

Among Vidal’s themes in the film, and his books, is that of America as empire, and his warnings – “as Pericles pointed out” – of empire’s overstretch and decadence; “prescient by 45 years”, says Gordon. Buckley meanwhile likened the hoisting of a Vietcong flag by protesters outside the Democrat convention of 1968 in Chicago as akin to flying a swastika.

As part of ABC’s coverage of the police “blue riot” that ensued in Chicago – batons cracking student skulls – Vidal calls Buckley a “crypto-Nazi” for justifying the brutality, to which Buckley snaps: “Listen to me you queer, stop calling me a crypto-Nazi or I’ll sock you in the goddamn face and you’ll stay plastered.”

The jagged clarity of the antagonism that leads to this moment when the banks burst, and the intellectual rip-tide beneath it, contrasts, says Gordon, with both present-day obfuscation – whereby politicians, columnists and TV presenters slither around, or just ignore, the themes of imperialism and American power – and also the banal, “ritual shouting matches” to which viewers of CNN, Fox, BBC and others are now subjected.

“It has to do with the corruption of debate,” says Gordon. “The conflagration between Buckley and Vidal was like a forest fire in the redwoods: huge old wood burning with depth. What you see now in supposedly antagonistic discourse is flash paper, it leaves no ash. Now people can be bought; now, the discussion ain’t really for the sake of the nation, it’s about personal gain.”

In one chilling line, writer and commentator Eric Alterman says the discourse between Vidal and Buckey is “harbinger of an unhappy future” for America – which of course it is. But Gordon rejects any notion that his project is nostalgic, insisting that his film’s appeal shows “a hunger out there for quality debate of ideas, and the word I’ve most heard used to describe the film is ‘delicious’.

“In a way, Hitchens was the last of his kind,” he says, “but there’s Andrew Sullivan, with whom I don’t always agree but find compelling; David Rieff – what would happen if he aired his views against his adversaries? And Sam Tanenhaus, Buckley’s biographer; when he and Hitchens said they were interested in our project, we knew we not only had a film, but a great film. We interviewed Hitch two weeks before his diagnosis [with terminal leukemia].”

Gordon continues: “It’s a wishful fantasy I have for the effect of the film. Nowadays, the issues at stake are the future of the planet, and it would be a brave move by a TV network to do what ABC did back then, perhaps in desperation. Get the thinkers out into the open like Vidal and Buckley, a really radical idea, against the grain.”

MIND GAMES: GREAT INTELLECTUAL CLASHES

Plato v Aristotle

A clash between two ways of how to approach understanding of the world: mystical idealist and methodological, which would become scientific method.

Leibniz v Newton

Bitter dispute over who – and whose country – could claim the invention of calculus; Gottfried Wilhem von Leibniz had written first, in 1684, before Isaac Newton’s Opticks, of 1704.

Freud v Jung

A row between erstwhile mentor Sigmund Freud and pupil Carl Jung, during a series of lectures in 1912, regarding the human unconscious, the origins of neuroses, dreams and sexuality.

Vavilov v Lysenko

An argument that took on vicious political connotations in Stalin’s USSR over the nature of genetic and environmental matters, focusing on Nikolai Vavilov’s work with plants. Stalin backed the anti-genetic Trofim Lysenko, and Vavilov died of starvation in jail.

Camus v Sartre

A rift at the heart of French existentialism and leftwing politics, between friends who split bitterly over France’s role in Algeria and the independence movement, and the nature of the individual and mass politics – between Albert Camus’s humanism and Jean-Paul Sartre’s Marxism.