The lawsuit isn't about Fortnight. It's about the Epic's own app store.
If you read the complaint, Epic is seeking to open their own app store on iOS and iPadOS devices called Epic Games Store. They are claiming that since Apple rejected this, they are being anti-competitive.
"Apple has enforced these restrictions against Epic. Epic approached Apple to request that Apple allow Epic to offer its Epic Games Store to Apple’s iOS users through the App Store and direct installation. Apple’s response was an unequivocal “no”." (page 22)
Today's stunt was undeniably staged, particularly since it coincides with Epic's offering of Troy: Total War (an Epic Games Store exclusive) free of charge for today only to help promote their nascent platform and Macs and PCs.
However, this doesn't detract from the idea that Apple is (quite clearly) violating the Sherman Anti-Trust Act of 1890, which Apple willingly subjected themselves to by creating and operating a marketplace. They've likely been in violation for the past 10 years, but nobody had the resources to mount a legal challenge. Just like the Browser Wars of the 1990s, the courts will likely give Apple the same options it gave Microsoft: Apples can remove themselves from the situation by shutting down the App Store and removing all third party apps from iOS and iPadOS, or they can allow alternative marketplaces and payment processes to exist on iOS and iPadOS to comply with the law. Simply put, if Apple doesn't want to play by the rules, it should exit the US market and enter new markets where US laws don't apply.