Take a classic Elizabethan play about a man who sells his soul to the devil, give it a modern-day twist as a satire on celebrity, and cast a pretty actor who shot to global fame in Game of Thrones. Seems like another smart idea by director Jamie Lloyd, who has form when it comes to hip stagings of classics with canny casting.

Alas, Kit Harington - Jon Snow of GoT - cannot carry this play. It's not for the want of trying: he does so much acting. So much. Not a line goes by without an accompanying grand gesture, hands twitching away; he minces and flops and broods, but his high declamatory delivery actually means speeches fail to register. The famous pout is much in evidence, presumably meant to convey moral anguish but usually coming across more Blue Steel. This seems an overly-strenuous performance, in a production bogged down by its many attempts to find a modern and edgy take on Christopher Marlowe's play.

The angels and devils that try to sway Faustus seem culled from a horror movie - twitching zombie-like figures wearing grotty underwear or often just bollock-naked. Mephistopheles and Dr F have a sexual attraction - something that's there in the text - but it isn't really explored, and it is cross-cast, Mephistopheles played by Jenna Russell. Lucifer, meanwhile, is a loud-mouthed Glaswegian who takes heroin, which just feels a bit Nineties try-hard.

And the whole show has a soulless sexuality to it, bodies and holes another representing another empty thrill. That's a reasonable point to make, but its chaotically inconsistent: sometimes there's a Carry On humour to the sex, sometimes its disturbing.

Also, Lloyd needs to be a bit cleverer if it wants to lampoon sex as a commodity, given they take full advantage of the obvious box office appeal of Harington. He's in tight pants for the vast swathes of it, shows off his bum, gets in the shower... of course, Harington has an amazing body, with the sort of sculpted abs that'd have a Ken doll reaching shyly for the towel. But if a glamorous female lead spent this much time in her bra, we'd definitely cry objectification. That could be an interesting tension; here, it just seems like Kit's getting his kit off to ensure a gossiped-about hit.

The problem is partly the play itself, and the problem with the play is two-fold: Doctor Faustus has famously unfunny middle scenes. This version, first seen at West Yorkshire Playhouse in 2013, replaces them with modern scenes by Colin Teevan, with Faustus as a celebrity magician, chasing fame and - ick - mired in a feeble, boringly conventional rom-com plot with his assistant Wagner (also turned into an attractive young woman, natch, to keep things heteronormative).

Faustus as an illusionist with no real talent: that really works. But these scenes still aren't funny, never quite finding their pace. The show is caught between being deep'n'meaningful - choose real love! do something valuable! - and going after cheap laughs in a cynical celebrity satire: dim groupies are mocked and groped, bankers are greedy, fame is empty. Even the heart-felt bits are weirdly undermined with sit-com canned laughter, cheesy music or cartoonish sound effects.

Harington seems to have been directed to play Faustus as a particularly vacuous chump (at one point, he reads a Mary Berry baking book in search of spell). Yes, Faustus trades his soul for so many cheap tricks, but this can be off-set against some justifiable lust for knowledge or anarchic spirit; Faustus is often an anti-hero. If he's shallow and dim from the start, why do we care about his downfall? We don't.

Much of the show is delivered with an impressively manic energy in the caperings of angels and devils, and Russell plays Mephistopheles as a steely, grinning figure. A fine actor, she seems at sea in this rudderless show; it pains me to say it, but the best bit is her interval entertainment, where she belts out a karaoke version of "Bat out of Hell".

Doctor Faustus was meant to work like magic: hot actor, hot ticket. Instead it's just a hot mess.

Doctor Faustus runs at the Duke of York's Theatre until 4 June.