In a radical configuration of the Royal Court's Theatre Upstairs, the audience sit in the centre of three sides of a narrow, cool green walkway, on stools that gently revolve, so we can watch the five actors who pace the narrow space, drawing intermittently on the walls in chalk, saying their lines to one another over the audience's head.

It's a disconcerting experience, as unsettling as the way that Debbie Tucker Green's words spool from their mouths, like inflected lines of the most patterned poetry, at once heightened and yet utterly true to the rhythms of normal speech. But as the words flow over 80 minutes, the piece comes together with audacious clarity. You understand everything about these lives as you follow the intricate web woven just above your eye level.

This is a play about love, and death and the way illness and grief can curdle and destroy even the strongest feelings. The details it provides as it charts these five inter-related lives range from the mundane – the way sex becomes boring – to the metaphysical – an ingrained inability to say sorry. The play's scope ranges from the destructive way a woman cannot talk to her husband in the 10 months after her mother's death, to minute skirmishes over possession of the TV remote control.

Its power springs in part from the contrast between its poetic telling and the daily realities discussed, such as the need to have a lock on the loo door to preserve some privacy or the exposure of undressing in front of a spouse. It is delicately directed by Green herself, with designs by Merle Hensel and lighting by Lee Curran that perfectly underline its pared-back simplicity. And it is performed – I saw its final preview – with a finesse and subtlety that makes it entirely engrossing.

You can't take your eyes off Gershwyn Eustache Jnr and Lashana Lynch as B and A, the leading couple, whose intimate relationship dominates the telling. Meera Syal, Gary Beadle and Shvorne Marks have less to do, but bring the same quality of precision to the language and their characters. Every feeling, each thought is recorded in a flickering play across their faces.

It's not easy viewing; you have to concentrate on the words and their shifting stories. But it is haunted by a deep emotional tug. Its lengthy title perfectly describes what happens in front of our eyes. It is very moving and very fine.

A Profoundly Affectionate Passionate Devotion to Someone (-noun) runs at the Royal Court until April 1.