Since its premiere in 1983 – in Britain, at the National Theatre, oddly – David Mamet's gimlet-eyed study of desperate real estate brokers selling a distorted version of the American dream has become one of his most popular and most performed plays.

Perhaps that has something to do with the fact that its savage view of the kind of capitalism that sets a group of grown men at each other's throats to come top of the "board" and win a Cadillac or pay their daughter's medical bills has grown more relevant with every passing year. Perhaps it's because its portrait of the group dynamics of the protagonists arguing about what it is to be a man is so compelling.

Or maybe it is simply that its tightly-strung dialogue that perfectly catches the rhythm and lilt of salesmen's patter offers irresistible opportunities to its all-male cast. In this revival, they are led by a seemingly ageless Christian Slater as the smooth-talking alpha salesman Ricky Roma, a man who can turn a chance encounter into an opportunity to offload a vision and a patch of dodgy real estate. He'd fit perfectly into Donald Trump's America, where they venerate the art of the deal.

His mentor Shelly (Stanley Townsend) has lost the gift and fallen on hard times. The play opens with him begging the smooth office manager John (Kris Marshall) for some "leads" - the all-important potential clients who might decide to buy prime estate in Glengarry Highlands or another development. The play pivots on this tightrope between success and despair, the elation of the sale and the desperation of failure.

At this distance, you can appreciate the poetry of Mamet's Pulitzer-prize winning writing, the way the three opening scenes, all set in a Chinese restaurant beautifully conjured by Chiara Stephenson's set, feature one pattering character and one almost silent stooge, whose interpolations punctuate the sharp, ceaseless phrases. The second act, set in the sales office trashed by a burglary, plunges into the consequences triggered when there is no morality beyond the pitch.

Yet this production, directed by rising star Sam Yates, doesn't dig very deep. It seems so in love with Mamet's words, with the way they ebb and flow that it skates along the surface of them, losing their passionate meaning. When Shelly pleads with John to give him a break and is greeted with a brusque "F**k You", it should count for something. It is the harsh underside of the free market expressed in two phrases. Yet here in Townsend's oddly one-note performance it passes for nothing except a quick laugh.

As Roma, the part Al Pacino played in the 1992 film, Slater has a lot of energy but he never seems to believe what he says. Roma should hold the audience, like his clients, in the palm of his seductive hand; Slater keeps it at bay with a breezy smile. The best performance comes from Robert Glenister who endows the floundering Moss with righteous fury and a pent-up rage. Don Warrington is quietly effective as the washed up George.

But in the end, this is a lively but overly polite version of a great American play that pays it respect, without ever illuminating its dark and passionate heart.

Glengarry Glen Ross runs at Playhouse Theatre, London from 9 November 2017 to 3 February 2018, with previews from now.