If you are on Windows and see Sign-In with Apple, Apple asks you to sign into iCloud, on their servers, if you are not already. It's almost the exact same sign-in flow you would see on Windows iTunes or Windows version of iCloud. You use your normal iCloud account information and 2FA verification (authorize the login in one of your Apple devices). Apple's servers look up the generated app-specific email address for you, just like your Apple device would, and passes that on when it passes the authentication token to the requesting application (which would use the same application identifiers it uses on iOS).

It's no worse a user experience than Sign in with Facebook or Sign in with Google, and in most ways it is the exact same user experience: click the button, get an Apple sign in prompt on Apple servers, sign in, get automatically redirected back to whatever app needed the sign in.