When season 4 of “Fortnite” launches Thursday, players like David Morell won’t be able to log into the popular videogame from their iPhones.

Mr. Morell, 32 years old, would first need to download the latest version from Apple Inc.’s App Store—but it’s no longer there. Apple and Google removed “Fortnite” from their app marketplaces earlier this month after the game’s creator, Epic Games Inc., added an unauthorized payment system that skirted the tech giants’ 30% commission on in-app purchases.

…