It's not every revenge tragedy that still springs a surprise, but James Shirley's play The Cardinal has barely been seen for 350 years. Written in 1641, just before Oliver Cromwell closed the theatres, and revived almost as soon as they re-opened, Shirley's play – his best, he believed – now seems like a literary loss. In Justin Audibert's compact production, it looks every bit the equal to its contemporary classics: Kyd's Spanish Tragedy or Webster's Duchess of Malfi.

Some 600 scripts survive from the 17th Century, yet only a select few make the stage today. Three years ago, the Royal Shakespeare Company tried a few out in workshops, pushing John Ford's Love's Sacrifice through to production. The Cardinal, which made the final four, might have made the better choice.

It revels in dastardly bastardry. The Cardinal himself, not half as saintly as his scarlett robes suggest, is a Machiavellian with the ear of the King, who plots to ensure the Duchess Rosura marries his nephew, Colombo. She, however, can't stand the man, preferring one of Colombo's colonels instead – a choice that triggers a tragic cycle of revenge.

That Shirley splits the scheming down the middle – the Cardinal closing in, Rosaura one step ahead – makes this particularly watchable, and each half culminates in a shocker of a set-piece, season-finale style. In Rosura, it has a fine female lead – a headstrong woman, in love, capable of outsmarting the society that would hem her in.

Audibert treats the play like the rare text it is. His plain-stage, period dress revival – think an RSC Swan show in miniature – is equivalent to handling the script with white gloves, wary of leaving the slightest fingerprint on it. A hands-off approach is understandable, giving a long-lost play a full and fair hearing, but ultimately unhelpful. Not only does it respect every scene in full, rather than steering an audience through the play, the old-fashioned style stops Shirley's set pieces from landing full-strength, sapping the violence at the heart of the play.

Instead, language is left to do the heavy lifting. That's a big ask: an unfamiliar plot in an alien style is hard work. At best, it's brow-furrowing; at worst, confounding. Without the sort of A-grade actors that make meaning as easily as they exhale, just keeping up can be exhausting. Audibert only has a couple at his disposal.

As such, his production makes space for Shirley's play without ever making a case for it. We get the gist, but none of the force – and, given how much it has to say to our times, that's a real shame.

This is, after all, a play full of dissemblers; a world in which everyone adopts a front to secure a free pass. Stephen Boxer's Cardinal is a wolf in saint's clothing, whose robes give him status and shake off suspicion. If he's shady in red, Natalie Simpson's superb Duchess Rosaura uses mourning dress to ward off admirers and conceal her affair. Elsewhere, best men turn backstabbers and antidotes prove poisonous.

What could be more 2017 than that? Shirley was writing in trust-no-one times: a civil war looming into view, a ruling establishment out for itself, a rebellious faction biding its time. For us, it's billionaire populists, reconstituted fascists and politicians spinning soundbites like broken records. After 350 years, it wouldn't take much for The Cardinal to land. Would another revival be too much to ask?

The Cardinal runs at Southwark Playhouse until 27 May.