You can practically smell the man-sweat dripping off director Sam Gold’s radical revision of “Othello,” whose high-profile actors, Daniel Craig and David Oyelowo , appear in a limited (and sold-out) Off Broadway run — produced by New York Theater Workshop with the additional backing of James Bond franchise producer Barbara Broccoli . The high-concept treatment updates the classic drama by transporting the action to a modern-day army camp. In this barracks setting, Shakespeare’s great military hero, Othello (Oyelowo), is unmanned and undone by the treacherous Iago (Craig) in full view of beefed-up soldiers wearing army-issue camo and big, black boots.

New York Theater Workshop has transformed itself to accommodate Gold’s innovative vision. The theater has been sheathed in rough, unfinished pine, and the auditorium seats replaced with steep, wooden bleachers — the better for an audience of voyeurs to peer down on the dozen or so soldiers preparing to crawl onto their floor mattresses for the night.  Everybody’s in tip-top shape (including the women), bulging with muscles and oozing testosterone as they have one last drink, play one more hand of cards, do a few more reps with the free weights, and playfully knock each other around.  (Props master Kathy Fabian earns a military salute for all the realistic junk strewn about the barracks.)

But when the lights go out, they literally go out, and the entire first scene is played in the dark (which goes on too long). Into this darkness creeps Iago (Craig, in velvety voice), to inform Brabantio (Glenn Fitzgerald), an influential Venetian senator, that his daughter, Desdemona (Rachel Brosnahan), is “making the beast with two backs” with the Moorish army general. That, of course, is the beginning of the end for these fabled lovers, who come to a tragic end when the traitorous Iago convinces Othello that his loyal, loving wife has been unfaithful with his top lieutenant, Cassio (a sympathetic performance from Finn Wittrock).

Drawing on the production’s powerful military vibe, both stars take their characters into primitive territory. Oyelowo makes a fierce Othello, using his imposing physical presence and resonant voice to reduce this noble character to a more primal state. But even after Othello is reduced to a murderous rage, Oyelowo tempers his brutality with remnants of his gentler spirit, drawing him to his tragic end — and the immortal dictate to “speak of me as I am … of one that loved not wisely, but too well.”

Craig, meanwhile, takes advantage of his military surroundings to add another dimension to Iago’s character. He’s still the sly villain who takes abstract delight in the destruction of his victims. He certainly works his cunning ways on Desdemona’s hopeless suitor, Roderigo (Matthew Maher, perfect), turning the poor gullible dupe into a bloody murderer. And in Craig’s performance, the character has acquired a powerful physical presence — and a steely stare — that also makes him physically threatening.

Craig’s Iago has a manner of detachment that underscores his outsider status. But while his subtle mind is too complex for the military life, he seems to envy the soldier mentality in Othello, to the point of identifying with the man he will destroy. “In following him, I follow but myself,” he says. “I am not what I am.”

The female characters — dressed (by David Zinn) in present-day duds and speaking with the careless diction of present-day youth — are the only ones not well-served in the production’s military environment. Brosnahan is as sweet as she can be as the innocent Desdemona; but in the guise of a modern young woman, she comes across as an incredible fool.

In the same way, Marsha Stephanie Blake’s rousing feminist take on Emilia (“Lay you down and roar!” she commands Othello) is a real pick-me-up at the end of the play; but it feels completely out of character. Not that this should matter to the youthful audience being courted by NYTW with this novel production — that they probably can’t get into, anyway.