So there I was, sitting in the vast Coliseum Theatre in central London, watching the sumptuous stage version of Hayao Miyazaki's Spirited Away, and wondering why I wasn't more involved in it. One obvious possibility is it wasn't made for me. I'm the kind of viewer Miyazaki despises, a grown-up who's wasted his life rewatching Spirited Away too many times when I should have been outdoors cleaning a river. If I can't feel the magic any more, that's tough.

The odd thing, though, is that I was beguiled by another recent Miyazaki stage adaptation, My Neighbor Totoro by the Royal Shakespeare Company, which will return to London next year. The Totoro play makes many changes to the source material, while Spirited Away is far more faithful. And yet the Spirited Away play feels fundamentally different from its source, much more than the stage Totoro.

I'm assuming readers know the Spirited Away film. If you know it well, you could follow the whole play without ever looking at the subtitles. That's something to highlight - this play has an all-Japanese cast and script, with English subtitles projected around the stage. There are three sets of subtitles to cover wherever you're sitting, two at either side of the stage and a third on top. I could read them fine, but often found myself not bothering as the script was so familiar.

The Spirited Away play is busier and more elaborate than the Totoro one, but some fundamentals are the same. Both plays make heavy use of puppets for the non-human characters, often moved by on-stage performers who don't hide themselves. Some effects are “simple” – for instance, characters transforming by going behind a curtained door from which new forms emerge. You can't predict which moments and characters will have the showiest effects. Some are wonderfully clever – for example, how the Stink God bath scene is done without water.

Like the film, the play is Chihiro's journey through strange places and characters. If anything, the Alice comparison is stronger than it was in the film version. There are deliciously strange moments where “inanimate” objects are played by actors with visible faces, like John Tenniel's Alice pictures or those weird old Fleischer cartoons where any knick-knack could come alive. The bathhouse regularly rotates and rearranges as the material demands, with Chihiro scurrying and climbing around it, while Joe Hisaishi's music fills the air; you'll know much of it from the film.

There's certainly magic. An object suddenly appears in the hands of multiple actors. There's an inspired way to convey Chihiro suddenly becoming, as she puts it, see-through; the play depicts it as a silent assault on her. One standout is Chihiro's first encounter with the fearsome Yubaba - and yes, as pundits have already noted, the autocratic ruler of the bathhouse in her aggressive blue dress and “off with her head” tones feels like a caricature of Margaret Thatcher. But she has the humour and humanity of the film's character too, and the cartoon power to spectacularly deform when a rage takes her. That's a splendid stage moment, both to see and to see how it's done.

But it also encapsulates how different the play feels from the film. On stage, we're watching a multitude of figures and effects. One of those figures is the girl Chihiro, but the creatures around her are so colourful that our eyes are inevitably drawn away from her much of the time. We watch her as one figure among many.

And that's crucial. In the film, Miyazaki quickly made us identify with Chihiro, to frame the world through her eyes. After all, she's the only human character after her parents' porcine transformation (which the play does pungently: the pig-parents are cartoony, grotesque and frightening). The film made us feel how alone Chihiro is when she's before something like Yubaba or No-Face, and the implicit terror in the title, Spirited Away. No-Face is often interpreted as a male predator, but you could read her as Chihiro's alter ego, lost and lonely.

The whole film was geared to letting us be Chihiro, in a scary wonderland. And that's what the play misses. Instead we watch a wonderland and lots of people milling around in it, including a girl. It underlines how different Spirited Away is from Totoro. That was about two sisters and their extended human family, including their neighbours, and then the Totoro would pop into the story like dreams that appear and vanish. But in the stage Spirited Away, the dream figures don't vanish; rather, they overwhelm the dreamer.

Without the framing through Chihiro's eyes, we take her journey without her, and all the play's ingenuity can't stop it feeling turgid at times. The film Spirited Away ran two hours. The play runs forty minutes longer, with much of that extra time taken by scene transitions, or by drawing our eye to the next clever effect. Stage magic is slower than the animated kind. Not all the effects work equally; there are several inelegant moments in the second act, images that don't work, diminishing the magic. There's so much going on that you can miss things – for instance, Chihiro receiving a gift from a divinity.

The Japanese cast is rotating through Spirited Away's London run. There's a provisional actor schedule here, though it's subject to change at any time. The performance I saw included the charming Mone Kamishiraishi as Chihiro. Many ANN readers will know her as Mitsuha, the teen heroine of Makoto Shinkai's your name., but the diminutive actress is perfectly convincing as a ten year-old grade schooler.

Other performers on the night included an energetic Tomorowo Taguchi as the spider-man Kamaji, thirty-five years after he took the title role in Tetsuo: The Iron Man by Shinya Tsukamoto. Yoko Ose, listed on the play's website as an understudy, makes an enjoyable and personable Yubaba, though I'd love to compare her performance to the other actors in the role– to the esteemed voice-actor Romi Park, and to the “real” Yubaba, Mari Natsuki, who voiced the character in the film.

The characters felt “right” on stage, though Atsuki Mashiko's had little time to make an impression as Haku. But lively as the performances were – and it was plain that Taguchi's and Ose's personal ebullience was coming through - there was little sense of them reinterpreting the characters, finding new sides. They felt tied down by the on-stage effects and the fannishly faithful script, in drastic contrast to the stage Totoro.

There's an extra gag with Kamaji, feeling almost like an ad lib, involving the spider-man's mass of hands. But it stood out oddly in a play with little room for such business. There are small embellishments – for example, a shadow character regarding Chihiro on the seaborne train, though it dilutes the focus on Chihiro in what should be her defining scene. The play's very last moments get tweaked interestingly, with a different emotional tone, and some viewers might prefer it to the film ending.

On the other hand, the play's first minutes are bewildering. Chihiro and her parents often have their backs to the audience, as if to say that Chihiro's not important after all. Moreover, any non-Japanese speaker is put at an instant remove from the actors, as you have to glance away from them to read what they're saying in the subtitles. The play has little room for intimacy. Even the memorable “eating onigiri” scene - where Chihiro recovers her selfhood through sadness, anticipating Pixar's Inside Out by 14 years – becomes a group scene with a supporting cast of flora, though it's very touching.

The most effective characters are bit parts, and not the ones that you'd expect. I was a little underwhelmed by several of the puppet characters, though one avaricious critter is great fun. A fantasy character from one of the film's last scenes is also vividly elaborated. But the quiet show-stealer turns out to be No-Face, performed by Hikaru Yamano. Whereas nearly all the characters are played by multiple rotating actors, Yamano is the only No-Face actor who's credited throughout the London run, barring an understudy.

No-Face's transformations are great, but its strongest moments are when the creatures's just being itself, dancing and stretching in ways that feel both sad and sinister. For once, the audience is granted intimacy with a single figure. And No-Face suggests what the play might have been, especially given the venue of the London Coliseum.

Spirited Away could surely be a ballet. You need only think of The Nutcracker– notably, Miyazaki himself adapted the source E.T.A. Hoffman story as an exhibit in the Ghibli museum. His film leaned into dance – think of the terrified Chihiro fleeing her pig-parents, bumping off ghosts. In the play, much of the activities of the bath-house are shown as dances, with Chihiro sometimes among the workers, humorously out of step.

A full Spirited Away ballet would still take us out of Chihiro's first-person perspective; but it would be a far freer adaptation, able to find new structures and meanings that a faithful adaptation can't try. And its star wouldn't be Chihiro, but No-Face.