Walking into the Culture Club in West Chelsea, New York, for a performance of Heated Rivalry: The Unauthorized Musical Parody last week, I was met by three ghosts left over from when the space was called the McKittrick hotel and it hosted the immersive spookfest, Sleep No More. The first was the phantom of clever detail: cans of Athletic IPAs for sale, a cute, non-alcoholic nod to the mega-popular series’ hockey setting. The second was of unnerving fright, as I realized there would be no booze at this singing satire. Would I be able to make it through 90 minutes of jokes about an overexposed Canadian gay sports romance, with zero quality guarantee and an even lower blood alcohol concentration? At least at the downtown premiere of the popular parody Titanique, long before it proved itself worthy of a handful of Tony nominations, you could stand up and order a bucket of White Claws.

But then the third specter materialized, the ghost of immersion and surrender, as this very funny production completely won me over. (I’ve since learned that a liquor license is forthcoming.) Heated Rivalry, for the uninitiated, is a television show adapted from a series of gay romance novels by Rachel Reid, a straight woman who unwittingly launched a thousand discussions about who gets to be horny over whom, how and when. Fans of the books petitioned for a wider release of the show produced for the Canadian streamer Crave, last November and, some six months later, its formerly unknown stars Connor Storrie and Hudson Williams are in easy contention for the most photographed people alive. Heated Rivalry: The Unauthorized Musical Parody is the latest addition to New York City’s musical parody cottage industry, which has led me to a theater lobby where a woman in a branded hockey jersey is telling the stranger next to her that she’s seen the series “probably not as many times as you think, but still a lot”.

There was a communal giddiness as everyone filed into the unassuming performance space, where less than 200 folding chairs were arranged around a small stage. Super-fans were giddy that their dreams were coming true, and the more reserved types, perhaps blushing at what they deemed beneath them, were still clearly enjoying themselves. I liked the TV show just fine, a bit underwhelmed at what was broadly discussed as “softcore smut” but felt more in line with the twee “naughtiness” of the romance world. I had worried a musical parody put together in a few months would be a cash-grab; plain fan service for those who can’t get enough of those six novels or episodes, not jabbing at the culture so much as stroking its ego. Impressively, as written by Dylan MarcAurele and directed by Alan Kliffer, it satisfies all three camps.

Framing is everything, and this romp begins with a faux earnest number, à la Waitress, where three suburban Susans detail their newfound pastime: putting their husbands to bed with some iPad time, knocking back an “Ambien margarita” and reveling in their favorite televised “boy aquarium”. From there, “Main Susan” (Ryann Redmond, glorious) recaps the years-long flirtation between the feuding players, innocent Japanese-Canadian “Shane Hollander” (Jimin Moon) and brusque Russian “Ilya Rozanov” (Jay Armstrong Johnson).

The obligatory double entendres (a song titled Shane Hollander, Slap that Stick! or a line, by Shane’s mom, about the “heavy load” her obviously gay son carries) are expertly delivered right between earnestness and tongue-in-cheek, but it’s MarcAurele’s ability to mock the story’s sillier elements that clinched it for me. Shane, whose thumb-twiddling submissiveness often grated me in the TV show, is played by Moon as a dopey bottom with a hopeless romantic complex. What the series plays out as a forbidden romance writ epic across timelines and borders, MarcAurele presents as Shane’s borderline delusion in dealing with an uncaring dom for years on end. “I keep replaying things he said,” Shane beams after a hookup, “like, ‘Ass up, little whore.’” The score’s best number, certainly the one best primed for cabaret nights anywhere, is Liza Minnelli’s Maybe This Time send-up where Shane croons, “This fuck felt different from the last fuck. This fuck, he asked if I would stay.”

If reading that inspires eyerolls – totally – Moon (and the rest of the cast, which includes Cherry Torres and Ryan Duncan) are so winning in their deliveries, so in on the joke without reducing their project into one, that it’s impossible to resist. As the icy-hot Ilya, Johnson has the less showy role and plays it mostly straight, which makes his song about an outcast childhood made tragic by his impossibly “big ass, cold heart” that much funnier. And, well, let’s face it: Johnson and Moon are sexy as hell, and charming to boot. Kliffer’s inventive staging, with choreography by Brooke and Tiffany Engen on a resourceful set by Sully Ross, goes long on bunny-hopping glee.

The Canadian Kliffer, previously artistic director of famed improv spots like Second City and Asylum NYC, where he helped launch Titanique’s improbable boom, later told me that these parodies rarely come together with such speed, let alone quality. He’d loved MarcAurele’s Pop Off, Michelangelo! in London and M3gan spoof stateside, and had just bought into Heated Rivalry, courtesy of its amorously optimistic fifth episode, when the writer texted him with the idea. The resulting work fits attractively between the out-and-out bawdiness of the Titanic send-up and the relentless Millennial nostalgia of Ginger Twinsies, which parodied the 90s Parent Trap remake last summer, and Kliffer notes that this very queer, very funny moment downtown – which also includes Cole Escola’s Oh, Mary! – points to “a little bit of an Off-Broadway renaissance. I think people just want to laugh, go out and have a good time, [and] see a show that is a little shorter.”

He also credits his improv background with inspiring Heated Rivalry’s audience participation moment, when someone in the front row is asked to portray François Arnaud’s obsessive jogger. (It was the actor Thomas Doelger at the performance I attended, briefly furloughed from his Book of Mormon gig while its theater bounced back from going up in flames. “You think a fire is gonna keep me from the stage?” he quipped afterward.) Doelger would certainly count among those who Kliffer said, “want to be together in a communal space and have fun with joyous people who aren’t afraid to be themselves”.

That last bit scanned as a bit of a platitude at first, but felt remarkably apt when I returned to the Culture Club a few days later to speak with expecting fans. Ashley, a 27-year-old public relations specialist, was there with Val, a friend she had talked into watching the series months ago. (“She got me,” the friend said, quoting Ashley’s pitch, “It’s gay, it’s really good.”) They didn’t consider themselves the target audience at first, but were drawn to a show prominently featuring “a gay Wasian”, as Ashley put it. Now it plays in the background, she says, “pretty much every time we hang out”.

Like most small groups in that pre-show holding area, those two were giggling to themselves, but I was immediately drawn to a woman heartily reaching out to others wearing jerseys similar to hers. Appropriately, she was a straight romance author from Connecticut, pen name Regina Kyle, there to see the show with her queer friend Lenny. Cutting off each other’s sentences, they explained his reluctance to watch the series, not wanting “another gay show where all we had was tragedy in the end”. A longtime fan of the books, Regina convinced him to dive in, the two grew closer, “and we discovered queer romance and that there was queer joy. That’s the whole reason Jacob Tierney made the show, right? He said we wanted more joy.”

• Heated Rivalry: The Unauthorized Musical Parody is at Culture Club, New York, until 7 September