There are coups d'état and there are coups de théâtre. Amy Draper's cabaret musical, first seen at Southwark Playhouse two years ago, combines the two. Using the conventions of burlesque and variety, These Trees are Made of Blood tracks the military uprising that ousted the Argentine president Isabel Perón in 1976 and the authoritarian junta that outdid her oppression over the next seven years. The revolution sours into repression.

The Coup Coup Club is in full swing. Our host for the evening, the Master of Ceremonies leading proceedings, calls himself The General. His gold epaulets and aiguillettes, not to mention all those spangling medals, make him as camp as Christmas, and Rob Castell guffaws his material like an old-school club comic. Backed by a four-piece civilian house band, he sings Darren Clark's witty revolutionary ditties: "Elections are unnecessary / When you lead the military." Imagine a putsch led by Noel Coward.

Around him, a glam Alexander Luttley swans around behind Argentine blue feathers, a pillbox cap over his little black corset, medals for nipple tassels, while Neil Kelso's military magician slowly hypnotises his audience.

In all this, Draper's concept thrives on the compelling side to cabaret. Like any crowd-pleasing art-form, it can manipulate its audience and, as it whips us into a frenzy, the line between collusion and coercion all but disappears. It's there in the General's MC patter: the question, 'What do you do and where do you come from?' demands answers; the knowingly awful jokes insist on groaned laughter. It's there every time an act nicks a cheeky sip of somebody's drink or sits, uninvited, on some poor soul's lap. It's in every 'volunteer' frogmarched onto the stage.

As such, the show sits on a slippery faultline. It never quite confirms its intentions as satirical or serious. Is Castell a performer lampooning a general or a general harpooning his audience? The ambiguity is superb. Is this subversive or oppressive? When camp fingertips extend into fleeting salutes, and veiled threats sit beneath cheery sing-a-longs, the humour starts to bare its teeth. As any number of alt-right trolls have shown, irony can mask a vicious intent.

However, that becomes punctured as an actual cabaret moves to an enacted drama. By introducing a level of fiction – a story about a disappeared protestor and the mother determined to find her daughter – Draper and writer Paul Jenkins let their audience off the hook. Not only is the narrative entirely generic, a way of illustrating the fate of dissenters tortured under the military junta, it reduces the in-the-room reality of the cabaret frame to little more than an aesthetic.

It's a shame. Individual turns convey the horrors and the history without the need for story. Luttley's spiked fan routine is as sharp as any instrument of torture, and Rosalind Ford's CIA striptease neatly illustrates underhand American tactics, while Clark's songs inform with wit. Instead, in reducing the junta's mass crimes against humanity to a single story, it lets the dignified, dedicated protest of the Madres de Plaza de Mayo – their white headscarves representing their missing children – slip into sentimentality. Not even Georgia Lowe's final design coup can bring it back from that brink. It's too manipulative by half.

These Trees are Made of Blood runs at the Arcola until 15 July.