Epic Games FAQ:

Apple will no longer allow users to sign into Epic Games accounts using “Sign In with Apple” as soon as September 11, 2020. If you have previously used “Sign In with Apple”, please update your Epic Games account email address and password immediately so that you can still login after September 11, 2020.

That’s tomorrow (Friday).

As much as it’s easy to say, this is all Epic’s fault, the issue remains that folks who signed up using Sign In with Apple are losing access to that privacy login mechanism, forced to jump through hoops to go to an alternative.

You might make the point that folks playing on other devices are not using Sign in with Apple. But, from Apple’s official SiwA support page:

Sign in with Apple is available with participating apps on Apple devices with the latest software—iOS 13 or later, iPadOS 13 or later, watchOS 6 or later, macOS Catalina 10.15 or later, and tvOS 13 or later—and with participating websites in Safari. You can also use Sign in with Apple with other web browsers and on other platforms, like Android or Windows.

So if folks bought into Sign in with Apple and use that sign-in across all their devices to get to an Epic game account, they still have no choice. According to Epic, they must move to an alternative login mechanism.