“Apex Legends” reached the 25 million mark in its first week, benefiting in no small part from the massive attention “Fortnite” has brought to the last-man-standing videogame genre since its launch in 2017. It took “Fortnite” more than a month to get to 20 million players.

“It’s the first crack in Fortnite’s armor and they’re taking it seriously,” said Doug Clinton, a managing partner at the investment firm Loup Ventures.

The battle for players’ hearts and wallets in the $100 billion-plus global videogame business has never been more pitched. PCs, consoles and smartphones give gamers more options than ever before, yet players are sinking their energy into only a handful of games. That makes it critical for publishers to make sure their titles are among the select winners.

In another mark of its popularity, “Apex Legends” became the most-watched videogame on Amazon.com Inc.’s live-streaming site Twitch within 24 hours of its Feb. 4 launch, according to Nielsen Holdings PLC’s SuperData. The game has kept that mantle nearly every day since.

Epic’s giveaway, which ends Feb. 27, is no coincidence, industry watchers say. The company is offering up a Battle Pass, a popular mix of exclusive costumes, dance moves and other virtual goods, to “Fortnite” players who complete certain challenges—meaning, gamers who spend more time in the game. A Battle Pass usually costs around $10. Loup Ventures estimates the promotion will represent lost revenue in the low tens of millions of dollars for Epic.

An Epic spokesman declined to comment on the giveaway. The company said 7.6 million people were playing “Fortnite” at the same time last Saturday, the most at any one time excluding special events.

The surprise success of “Apex Legends” after nearly two years of secret development—many people inside EA didn’t even know it was in the works—couldn’t have come at a better moment for the company. A year of “Fortnite” dominance had left makers of other games scrambling for a response—and frustrated that even their successes at times seemed to fall short.

Earlier this month, EA reported disappointing holiday-quarter earnings, and its stock sank more than 17%; it has since recovered. Activision Blizzard Inc. said it failed to meet its own expectations in 2018 and would cut about 8% of its workforce in a broad restructuring. Take-Two Interactive Software Inc. sold more than 23 million copies of “Red Dead Redemption II” since its release in October—by all measures a blockbuster—but its shares have fallen on management’s soft outlook.

Take-Two and Activision Blizzard declined to comment.

Keeping mum about “Apex Legends” was a change for EA. It didn’t tease the game at the closely watched E3 videogame conference in June, as it has done for past big releases. There were no pre-launch ads, preview trailers or social-media posts.

Instead, EA paid several influential gamers to play “Apex Legends” live on Twitch shortly after its stealth launch. They included Tyler “Ninja” Blevins, a celebrity gamer with more than 13 million Twitch followers who last spring helped propel “Fortnite” to fame when he live-streamed a game session with recording artist Drake. EA declined to say how much it paid the “Apex Legends” streamers.

Dean Crutchfield, chief of branding firm Crutchfield + Partners, said it is becoming more common to pay popular streamers, but the tactic could backfire if body language reveals they aren't enjoying a game. “You can’t control how people behave,” he said.

In keeping the “Apex Legends” development hush-hush, though, EA avoided repeating past blunders in rolling out new games that drew negative attention, BTIG analyst Brandon Ross said. Last year, EA delayed the launch of its big holiday release, “Battlefield V,” to make changes based on early feedback from players who tested it. More recently, EA was thumped on social media by some players who got early access to “Anthem,” a new action role-playing game, and said it was riddled with technical problems.

“Using influencer marketing made a lot of sense because ‘Fortnite’ players were very attached to these streamers and would be open-minded to at least trying the game,” Mr. Ross said. “They captured the audience they were targeting.”

Epic and “Fortnite” haven’t been standing still. Earlier this month, the game staged a live, 10-minute concert with the electronic-dance-music artist Marshmello. That followed a day last spring where “Fortnite” players could turn their avatars into the Marvel Comics supervillain Thanos.

The special events give people new reasons to keep playing. “The name of the game is to keep players engaged,” Mr. Ross said. “The launch is just the beginning.”

Write to Sarah E. Needleman at sarah.needleman@wsj.com