Then, the videogame retailer’s stock crashed—and crashed hard. Within days, it appeared Mr. Misener’s hopes for big gains had evaporated.

Mr. Misener’s story could have ended there. Instead, in February, as GameStop’s stock careened toward $40, Mr. Misener did what at the time seemed unthinkable: He kept buying. Amid the wreckage, he started discovering there was a lot to like about GameStop, he said. He bought in again, and again—seeing it as an investment in the company’s future.

Today, Mr. Misener has earned more than $18,500 in paper profits from his GameStop position, buoyed in part by a surprise resurgence in meme stocks over the past two weeks. GameStop,

AMC Entertainment Holdings Inc.

AMC 18.63%

and other stocks popular with individual investors on social media have soared and swung wildly in recent sessions, even as the broader stock market has been stuck in place.

The S&P 500 logged a modest 0.6% advance last week, while GameStop climbed 12%, building on the previous week’s 26% rally. With an outperformance like that, many individual traders say, it is hard not to be loyal.

Mr. Misener is one of several traders who have transformed into GameStop true believers, amassing large positions in the stock, with no intention of selling soon. Some, like Mr. Misener, had never stepped foot in a GameStop store or spent much time playing videogames. Now, hardly a day goes by when GameStop isn’t on their minds.

Individual investors’ gamble on GameStop earlier this year has often been framed as an impulsive, adrenaline-fueled bet, led by hordes of online traders on Reddit’s WallStreetBets forum. Many don’t deny at least some of that’s true. But many say they have also turned their positions into an opportunity to get in early on a company that they expect will look drastically different in a year’s time.

“Tesla had naysayers and

Amazon

had people who were against it, but it’s those two companies, and now GameStop, that are transforming a whole mind-set and methodology for how to do business,” said Mr. Misener, a manager at a technology-services company. “This could be huge.”

Driving that theory for many individual traders is one man who has climbed quickly through GameStop’s ranks:

Ryan Cohen,

the co-founder of pet-supply retailer Chewy Inc., who has ascended within months from GameStop’s activist investor to the company’s nominee for chairman. Though only in his 30s, Mr. Cohen has been called an e-commerce wunderkind after selling Chewy to PetSmart Inc. for $3.35 billion—the largest-ever e-commerce deal at the time.

Many individual investors are betting Mr. Cohen can replicate that success at GameStop by steering the company into the digital age and away from years of declining revenue and failed experiments. As evidence, some point to GameStop’s recent hires with ties to e-commerce, as well as Mr. Cohen’s November letter to GameStop’s board. In that, he emphasized the need for GameStop to become a “technology-driven business” that offers competitive pricing, broad gaming selection, fast shipping and strong customer service.

In a recent securities filing, GameStop acknowledged the need to respond to the shifting landscape. Making the transition, however, won’t be easy, especially in an industry that is growing increasingly competitive.

Like other companies, including its meme-stock companion AMC, GameStop is emerging from the challenges of the Covid-19 pandemic with a loyal band of shareholders that it didn’t have a year ago—some of whom could transform into customers. AMC in particular has tried to capitalize on that, announcing last week it would reward investors with a free large popcorn when they attend their first movie at an AMC theater this summer. A day later, however, the movie-theater chain warned investors of the potential for big losses due to the volatility of its stock.

Both companies have taken advantage of the meme-stock mania by selling more stock to strengthen their balance sheets. GameStop also announced recently it had taken steps to eliminate its long-term debt.

Many skeptics in the market have warned that a meaningful transformation will take time and that the company has yet to reveal much about specific next steps for how it will reinvent itself. They also have cautioned that GameStop, on a fundamental basis, isn’t worth its current stock price. GameStop shares closed Friday at $248.36, a more than 1,200% increase in 2021 that gives it a market value of roughly $17.5 billion. In contrast, Michael Pachter, a research analyst at Wedbush Securities, has a $39 price target and a sell rating on the stock.

“There is a disconnect between fundamentals and valuation,” Mr. Pachter said. “And Ryan Cohen still hasn’t told us what his strategy is. This business is completely different than dog food.”

Unlike pet supplies, which are typically recurring purchases, Mr. Pachter said, videogame customers don’t tend to buy with as much regularity. Plus, he noted, GameStop still has a vast network of roughly 4,800 stores—and recently announced the coming departure of Chief Executive

George Sherman,

who came from a background at other retailers with bricks-and-mortar businesses. Its chief financial officer and other executives also departed this year.

Many individual investors say Mr. Cohen’s bold approach with GameStop leadership is what earned their trust. It also simultaneously thrust him to celebrity status on forums like WallStreetBets. There, users frequently call him “Daddy Cohen,” while swapping ideas on the meaning behind his cryptic tweets. One late February tweet, of a frog emoji and a picture of an ice cream cone from

McDonald’s Corp.

, sent individual investors into a frenzy and coincided with a 104% one-day jump in GameStop shares.

“It’s obvious that he’s been on the Reddit pages, he’s posted stuff on social media, which shows he’s engaging with investors and what they want,” said Thushira Kumarage, a 21-year-old student in Edinburgh who bought GameStop stock in January at the recommendation of friends. He holds about 180 GameStop shares in his brokerage account, steadily adding more from time to time.

Individual investors say they will be closely watching Wednesday’s first-quarter earnings report in which GameStop is expected to report higher sales from a year earlier, thanks, in part, to the release of new gaming consoles late last year. Many say they will also be watching for any clues out of the company’s annual shareholders meeting the same day.

Some investors said they anticipate that GameStop’s share price could be volatile around Wednesday’s events, especially after last week, when it swung in a range between roughly $227 and $294.

“My thoughts are incredibly unwavering—I like the company,” said John Evans, 21, who first bought GameStop shares around $14 in December at the recommendation of classmates at the University of California, Santa Barbara. He has since added to his position, including on the stock’s volatile days and expects to hold a few shares—potentially forever—for sentimental value.

After all, he said, it has been a wild ride—and he is up nearly $40,000 on his GameStop positions.

“I’m definitely going to hold,” said Mr. Evans. “I think you can say that to a reasonable degree, this captain will go down with this ship.”

Write to Caitlin McCabe at caitlin.mccabe@wsj.com