Nearly all the drama in Tom Morton-Smith’s new play is drawn from Bobby Fischer. Mercurial, petulant, paranoid and Jewish — the loose-cannon reputation of the chess genius, who in 1972 squared up to Russia’s reigning world champion Boris Spassky, is reinforced in this account.

The action is set mostly in Iceland — the location of this titanic encounter and a country seen as neutral in the Cold War. Ronan Raftery’s Spassky is cucumber cool when we first meet him, the unflustered core of an otherwise jittery Soviet entourage waiting to see if Fischer will show up, let alone win.

As they wait, Fischer takes the first of a series of phone calls from Henry Kissinger designed to stoke the unpredictable chess player’s patriotism.

The Secretary of State’s instantly recognisable drawl — a terrific, offstage performance by Solomon Israel — reveals much that motivated the enigmatic Fischer, played by a wiry, intense Robert Emms. It’s a conversation about identity and loyalty, and Fisher’s question to Kissinger — “Are you Jewish?” — reveals that the politician’s prime allegiance is to his country. “I’m Jewish by birth,” he says. Fischer meanwhile rejects all allegiances other than to himself. His fight, it turns out, is against the chess establishment. The mentored and middle-class players that make up much of the chess playing fraternity viewed Fischer as some kind of “savant” because he’s a “poor boy from the Bronx”. In fact, he was just cleverer than them, is Fischer’s point.

In many ways, Morton-Smith’s play is a study of two opposite psychologies. But whereas the playwright’s 2015 work Oppenheimer got under the skin of historical events and figures, this one never seems to find the dramatic kernel that sustains his play.

Annabelle Comyn’s production is brimful of interesting scenes and encounters. The Russians’ frantic efforts to prove an American conspiracy when Fischer starts to win is one such. And the chess games themselves are conveyed with unexpected moment of physical theatre, with Fischer’s circling his opponent in his specially imported chair while Raftery performs Spassky’s mannerisms at the chess board in a blizzard of time-lapsed adjustments to his jacket. The technique works superbly well as way of condensing the period over which the tournament took place.

Meanwhile, Spassky’s attendant psychologist Nikolai (Rebecca Scroggs) is full of measured insight about East-West relations. Yet he is oddly immune to political stakes at play and so feels like a creation of today.

It is also not clear how the play benefits from cross-gender casting with Scroggs’s Nikolai on one side and Buffy Davis as American fixer Fred Cramer on the other. Perhaps cross-gender has evolved to the point where it doesn’t have to be justified.

Yet much of this distracts from the drama. It’s as if the production knows it has masses of fascinating material but lacks the urgent story with which to stick it together.