I’ve been trying to figure out the best word to describe American Crime Story: The Assassination of Gianni Versace, but I just can’t get a handle on it. At first I thought it might be “gay”, but that’s not right at all. “Gay” just means gay. It’s no more a vibe than “straight” is. Then I thought it could be “camp”, but that’s even more wrong. Most of the gay characters in this startling show aren’t remotely camp. They’re muscular, toned and dangerous, but also quite often dressed as Louis XIV’s lamé curtains. Best understood, I suppose, it’s a deep dive into the aesthetic of 1990s American homosexuality, in much the same way that American Psycho was a dive into that of 1980s Manhattan finance. Which is not, I’d imagine, quite what anybody expected.

Technically, it is also a sequel. The first series of American Crime Story was better known as The People v OJ Simpson, a show that won big plaudits and numerous awards, yet which was also, at least in my experience, oddly easy to stop watching. This, obviously, focuses on the killing of Versace in Miami in 1997 and could easily be very similar, with gawkers and a media circus and cops and lawyers on the make. It isn’t, though, and not only because its title character clearly has to spend quite a lot of time dead.

The focus is instead on Darren Criss, as his creepy killer, Andrew Cunanan. You may remember Criss from Glee, a show in which he was more inadvertently creepy as an exhaustingly kind and gentle enthusiast of musical theatre. If you ever thought to yourself, “Man, that Blaine guy could be a serial killer,” then it turns out you weren’t the only one.

Last time around, Cuba Gooding Jr and John Travolta led the cast. This time we have Penélope Cruz as a frankly odd choice to play Donatella Versace. I’m loath to be unchivalrous, but it’s like getting Brad Pitt to play John McCririck. Up against her, as brilliant as the whites of his own teeth, is Ricky Martin as Versace’s bereaved partner, Antonio. Versace is played by Édgar Ramírez. It’s a little odd to hear these three Spanish-speakers pretending to be Italian by chatting in heavily accented English, but a greater distraction is the way they’re all blown off screen by their backdrops.

Every shot that features any one of them is like one of those insane Versace advertisements with Madonna in them as a businesswoman. Remember them? She was always on the phone, halfway between buying half the FTSE and having an orgasm. I think it’s actually more of a mid-2000s Donatella aesthetic, that, than a 1990s Gianni one, but crikey, ask somebody else. It’s all bright lights, patterned satin, patent leather belts and expensive sexiness you’ll never afford. Pre-death, Ramírez wakes in bed and strides down corridors more glitzy than a Swiss chocolate box, across a patio decked out with so many houseboys standing to attention in shorts that it could be a Wimbledon tennis court. When the plot gets going, you’re almost sorry. You don’t want to think. You just want to watch.

Before long, though, and at least by the second episode (I’ve sneaked ahead; they let us do anything) it turns out to not be that sort of show at all. More interesting than Versace’s gaudy closet is the role he plays being so uncompromisingly out of it. Out in the wider world the Aids epidemic had only just passed its height and even George Michael wasn’t out yet. Mass acceptance — let alone equality in law — was still far away.

From his palace in Miami Beach Versace existed as a sort of approachable living saint of the local gay community, which itself seems to have been a collection of nomads, lost souls, addicts and pioneers, all of whom had made the conscious and probably painful choice to build their identities anew. The heroin addict Ronnie (an unrecognisable Max Greenfield, better known as New Girl’s Schmidt) is indicative of the more desperate flotsam this world attracts; Cunanan, although very definitely a fantasist and a psychopath, is its extreme form.

The easiest way to write a story is to take the first chapter of somebody else’s and see where your imagination wants to go. The Assassination of Gianni Versace may not go to all the places it feels it should, but that would be a shame. In the US, which is a few weeks ahead of us, it hasn’t quite been the hit of The People v OJ Simpson, but for my money it’s a whole lot more interesting. Apologies for the spoiler (look away now), but history tells us that Cunanan took his own life eight days after the murder. What did he do before? Who made him what he was? Callous as it may seem, we already know what happened to Versace. At its best, this isn’t about his assassination at all, but his assassin.

TV review: Hugo Rifkind on American Crime Story: The Assassination of Gianni Versace