This is not hell, nor are we out of it – to borrow a phrase from Doctor Faustus. Russian dramatist Mikhail Durnenkov makes a similar case in this collection of playlets about our divisive times. We're not at war, but nor is this peace. The whole world, he implies, has become a cultural battleground.

Written in the wake of the war in Donbass – in which Russia repeatedly denied any involvement despite 30,000 militias crossing the border to fight – The War Has Not Yet Started takes a figurative, sometimes surrealist, approach to the idea that constant conflict has become a new norm.

In 12 self-contained skits, Durnenkov tees up various 'us versus them' scenarios to suggest a state of permanent suspicion. There's the family zoned into their electronic devices to block out the clamour of the real world outside, and the peace protestor accused of an inflammatory act, his peaceful demonstration deemed to have stoked up tension and triggered violence. Bob Bailey's back wall mural entwines blue cornflowers and barbed wire, while Gordon Anderson's three-strong cast wear casual camo-prints and khakis.

Durnenkov keys into the world's loop-the-loopiness. In one skit, an ardent anti-smoking activist cheerily admits that life-after-cigarettes is a state of permanent resistance – an ongoing fight against the occasional craving. Smiling this insane fixed smile, Sarah Hadland makes clear that everything has changed. There's no going back.

In that, Durnenkov's play extends far beyond Ukraine's borders, reaching out into the world at large – from Brexit and Trump to Twitter trolls and thought crimes, all the way to a world waiting for its next terror attack. It's a play that gradually comes into focus, maybe even one you only fully understand in hindsight – by which time, it might even be too late.

Several sketches dwell on the conflation of fact and fiction – a bemused swimmer accused of adultery for fantasising about a fellow swimmer's wife; a newscaster knowingly broadcasting fake news. Durnenkov's point is that it's increasingly impossible to distinguish the two. Mark Quartley plays a robot with an absurdity implant to make him seem almost human – but he might just be a bit of an odd bloke. You can't tell the two apart – just as you can't tell militia from soldiers.

Trouble is, Durnenkov's skits are mostly inert. More illustrative than active, they lack a life of their own; too little at stake, too loaded with symbolism. Sat awkwardly on another show's set, Anderson's low-key production can't wring them for laughter, but nor does Noah Birksted-Breen's translation mine the linguistic potency of, say, Caryl Churchill or Harold Pinter's shorts. Durnenkov sneaks up on a slippery set of ideas, but his individual scenes are faintly absurd and fairly forgettable.

The War Has Not Yet Started runs at Southwark Playhouse until 10 February.