Let’s get this out of the way up front, because I’d like to be as charitable about Chess as Ruhl is about the way men have too often treated women: Euan Morton can sure as hell sing. He sings the bejeezus out of “Anthem,” the heart-stirring melody in which a defecting Soviet chess champion proclaims his unbreakable connection to the land he’s leaving. He sings sharply, opposite a manipulative KGB minder, about the fears and drives of a man at the top of his game; he sings tenderly, in concert with the silver-sopranoed Jill Paice, a duet about how hard it is to put love into words.

But here’s the thing: That duet, “You and I,” keeps circling back to the observation that Morton’s Anatoly and Paice’s Florence have “seen it all, chasing our hearts’ desire”—but it is by no means apparent, either from Richard Nelson’s oft-reworked book or from Eric Schaeffer’s streamlined but still flashy staging at the Signature Theatre in Arlington, what those hearts’ desires actually are.

As the story opens, why is Florence, a 30-something genius with a past shadowed by the 1956 Soviet crackdown on Hungary, in thrall to the bratty American chess master Freddie Trumper (Jeremy Kushnier)? Couldn’t tell you; there’s no obvious sympathy between them, nothing about him to suggest what makes her put up with his diva displays. Nor is there anything, on stage or on the page, to explain Florence’s transfer of her affections to Anatoly midway through the Bangkok phase of a chess championship that will, inevitably, bring all concerned back to Budapest before they’re done. (Speaking of Bangkok: The lurching, crotch-centric choreography on display when Trumper spends his “One Night In …” that famously loose Thai capital isn’t doing anyone any favors.)

Launched as a concept album, successful in a massive London production, but a legendary if cultishly admired flop on Broadway, Chess has always been a problem show. Schaeffer’s revival, the first major U.S. staging in many a year, strips away most of the political specifics and some of the spectacle of gamesmanship, preferring to focus instead on the people and their problems.

Understandable gambit, when fewer and fewer audiences remember the Reagan-Andropov era it’s set in, much less the decades of arcane geopolitical machination that preceded it.

But Nelson, along with songwriters Benny Andersson and Bjorn Ulvaeus—the ABBA veterans, whose melodies can be surprisingly sophisticated, even if they often seem to have little to do with the words Tim Rice has strung upon them—hasn’t given Schaeffer much to work with, and some of the newest revisions to the story move its conclusion away from the bleakly tragic toward the mawkishly sentimental. If the complicated maneuvers of the heart—and of the game that was once at the center of this musical—are what intrigue you, you’ll probably come away feeling unmoved. Go just for the songs, though, if that’s your thing; you’ll definitely come away with one on your lips.