The link in the email may or may not work that way - that would be down to how the authentication system has been designed. Some of them recognise that users a

The link in the email may or may not work that way - that would be down to how the authentication system has been designed. Some of them recognise that users aren't always signing in on the same device that their email account is set up on, so the link in the email just confirms that the login attempt is genuine. This is similar to how Google/Apple/Microsoft/Blizzard/Steam handle login requests with their respective authenticator apps. You attempt to log in on device X (which can be anything), then confirm that the login request is genuine on device Y (your personal device).