The important disclaimer can be found in the fine print of its freshly updated App Store Review Guidelines:
This pretty much means that once the Sign In with Apple service is out of beta later this year, third-party app developers will have to be ready with the implementation and must support it in their apps.
The benefit of Sign In with Apple is first and foremost privacy. At WWDC, the company stressed that unlike Facebook and Google, it does not collect any information and will not track you. It's also expected to be even faster than those sign-in services, allowing you to be signed in with a single tap (unless an app requires your email). And speed for logins is, of course, of critical importance for companies like Uber and Bird that users often need to quickly sign into.
The other benefit of Sign In with Apple is for those pesky emails that you start getting spammed with as soon as you register with a new app. Apple will offer you to automatically create a randomized email address that will forward those emails to your main address. This will allow you to quickly disable that random email and never be bothered with pesky email notifications.
We should also point out that this new sign-in option will be required for implementation IF the app uses social login and will not affect apps that use a native log-in solution.