Sleuth poses a bit of a conundrum to the critic. Anthony Shaffer's 1970 play is so absolutely dependent on its twists and turns, its dodges and reversals, that to say too much about it is to topple its carefully constructed framework of surprises. To offer even the vaguest outline of the plot, not to mention its multiple developments, is to risk spoilers.

Don't worry – I won't give the game away. I can't help, though, questioning the premises of the game itself.

It's not revealing too much to say that Shaffer's detective novel writing protagonist Andrew Wyke (Miles Richardson) is a big fan of games. Shut away in his Wiltshire mansion, he plays and constructs complex puzzles, preferring riddles to people. At the opening of the play, he has invited his wife's lover Milo Tindle (James Alexandrou) over to the house, quickly drawing him into a game that is, inevitably, not quite what it seems.

In the cat-and-mouse manoeuvring that follows, the two men struggle for dominance, countering one another with their wit and invention. Women, meanwhile, are reduced to playthings – offstage wives, mistresses, victims. They exist, like Andrew's wife, merely to be disposed of or fought over – or, at best, to act as plot catalysts. We are, it seems, invited to laugh at Andrew's behaviour (ha! misogyny!), but it's hard to cough up a chuckle with such a sour taste in the mouth.

The problem is that neither play nor production ever turns the tables on its protagonists half as well as they pull the rug out from one another. There's a hint of class critique to the clash between aristocratic Andrew and second-generation immigrant Milo, along with a half-hearted attack on Andrew's twisted worldview that arrives a little late in the day. But really, despite the nastiness it exposes, Sleuth strokes the egos of its male creators just as much as Andrew's games soothe his insecure masculinity. At its core, it's about privileged men showing off how clever they are.

And Sleuth can, admittedly, boast a certain degree of cleverness. While some plot twists can be guessed at, others come as genuine, startling surprises – thanks, largely, to the skill of Richardson and Alexandrou in sustaining the tension while not giving anything away. Barney George's intricate set, meanwhile, is all red buttons and revolving staircases, a fairground-like construction over which Andrew can – like the petty, impetuous child he is at heart – gleefully assert his control.

It's difficult, though, to see much of an argument for putting this on stage, now, like this. Even within the play, it's pointed out that Andrew's is a fading, dated world, one that harks back to an Agatha Christie era of grand country houses and aristocratic amateur detectives. Andrew's attempts to recapture this age even as it slips through his fingers are mocked somewhat, but the show's entertainment value remains firmly with the game playing that he nostalgically clings to. Giles Croft's production likewise struggles to offer anything more than nostalgia – a white, upper-class, distinctly male nostalgia that feels more tainted than ever in the wake of the Brexit vote.

The game, as another lover of mysteries might say, may well be afoot. But what's the point in it?

Sleuth runs at the West Yorkshire Playhouse until 15 October.