A golden glow illuminated the employees huddled inside a Hex & Co. cafe on the Upper East Side, a haven created for board game enthusiasts to gather for fantastical quests.

Meticulous campaigns were second nature to these workers — how many times had they infiltrated an obsidian castle or vanquished a warlock? They had been immersed in this particular adventure for months, navigating a labyrinth governed by strict rules and made harrowing by unfamiliar tasks and tests. Now they gathered to plot their final triumph: unionization.

On that Tuesday in September, Hex & Co. workers confronted their bosses with a demand for recognition. Less than two months later, they voted to join Workers United, the same group that has been organizing workers at Starbucks stores across the United States. The workers at the three Hex & Co. locations across New York City were just the first employees of a board game cafe in the city to unionize. Workers at the Uncommons and the Brooklyn Strategist followed this month.

All the stores fall under the ownership of either Jon Freeman, Greg May or both, and they pleaded with their employees not to unionize, saying that a union would wipe out the “flexible and open-door atmosphere we have tried to foster.”

Teaching board games is a far cry from swinging a miner’s pick or working numbing hours on an assembly line. In fact, many of the cafe workers said they hung out at their workplaces in their off hours. But in the end, complaints over dollar-an-hour raises and bands of unruly children reigned: Among the 94 employees who voted, only 17 dissented.

“There is not a group of people better at organizing than a bunch of nerds,” Jennifer Taylor, who works at the Brooklyn Strategist. “We’re all people who are hyper-focused and hyper-specifically excited about something, and we have a job doing that thing. And we’re going to fight to the death to defend that.”

Only 10 percent of American wage and salary workers were union members in 2022, a historical low, according to the Bureau of Labor Statistics. The food-service sector’s membership rate was less than 4 percent. But this fiscal year saw the most representation filings since 2015, according to the National Labor Relations Board.

Young workers “are willing to take risks, because they feel like their future is at stake,” said Kate Bronfenbrenner, the director of labor education research at Cornell University.

After slogging through a recession and a pandemic, many found themselves earning minimum wage while corporate profits soared, she said.

But Andrew Rigie, executive director of the New York City Hospitality Alliance, said that costs for food-service businesses, many scraping by on tight margins, had risen dramatically thanks to inflation. The group’s preholiday survey of 281 New York City restaurants and bars found that labor costs were the main concern for 72 percent.

“The pandemic just took what was a tough business environment and made it impossible,” Mr. Rigie said.

Tensions over pay and working conditions had been brewing at the city’s board game cafes before plans to unionize kicked off this autumn.

At the stores, customers can roll the dice in weekly Dungeons & Dragons sessions or play one of the games stuffed into bookshelves. In the afternoons, children cluster around tables in rapt attention as counselors explain the arcane rules for imaginary worlds.

But in interviews, workers said pay was low and staffing inadequate. Some described frantic scenes at birthday parties or tournaments that they had to oversee alone. Dungeon masters, who facilitate games, often did hours of unpaid prep work.

Sasha Brunetti, an 18-year-old Hex & Co. employee, said members hoped unionizing would add structure: “The owners aren’t great at rescheduling meetings or answering emails, or they make changes without telling us, like changes to the menu.”

Mr. Freeman and Mr. May did not answer telephone messages or emails seeking comment on the complaints. But in an October memo to Hex workers, they questioned whether a union was necessary. “It will lead to a more formalized ‘by the book’ relationship that is in no one’s interest except Workers United,” they wrote, adding that they had heard of employees being “coerced” into signing petitions.

Joseph Valle Hoag, 28, said he needed no coercion. He started at Hex & Co. as an after-school counselor, juggling two other jobs to supplement the $17 an hour he earned teaching board games.

Three months into his job, Mr. Valle Hoag was approached by another worker about organizing and Hex employees drafted a petition demanding better conditions.

“I would literally hang out outside of the shops waiting for people’s shifts to end, so I could grab them for a quick conversation,” Mr. Valle Hoag said.

A cadre of employees gathered after hours in Riverside Park, near the Hex location on the Upper West Side. There, they heard from Workers United representatives about the strict rules of the unionization game and mapped a strategy to win a binding contract.

So began the quest, and employees at other board game cafes in the city started organizing their own troops.

Christine Carmack, 28, helped assemble fellow workers at the Brooklyn Strategist.

“We met at a coffee shop nearby, and I remember how almost electrifying it felt every time a new co-worker came in,” Ms. Carmack said. Every person who had been invited showed up to the first meeting of what is now Brooklyn Strategist Workers United. One who had a dog-walking gig stopped by with the dogs.

“I’ve been riding that high for the last month and a half,” Ms. Carmack said.

On Sept. 29, having refused to voluntarily recognize the union, Hex & Co.’s owners filed for an election overseen by the N.L.R.B., and in November, the employees’ roll of the dice paid off. Members are now preparing to negotiate a deal and to shoulder union dues of $9 a week for those working more than six hours per week.

But for all that the employees said their workplaces lacked, the thought of quitting was just as unsatisfying.

Employees at the Brooklyn Strategist come to the store on their days off to participate in tournaments. At Hex & Co., staff members get together at musical events and parties — complete with board games, of course.

On a recent Monday night, Hex Workers United celebrated the election win at the Midtown offices of Workers United NY/NJ. Grease-stained paper plates of pizza and half-empty bottles of beer littered the tables. People flitted between card games and watching Zev Anderman, a 19-year-old employee, perform magic tricks.

“If an owner comes in and says, ‘We’re a family,’ you aren’t really going to buy that,” Mr. Anderman said. “That’s them trying to play nice so they don’t have to pay you more. But legitimately, here, I think we are a family.”