I applaud the attempt to move away from passwords, but this seems like a pretty annoying solution. I don't want access to my email to be tied to my access to "The Magazine". If I'm going to need to access some other service to log in, I'd prefer a Google Authenticator style solution where my access code is always a single click away from my phone's home screen. Maybe Marco/The Magazine could use Google Authenticator and just accept any password as long as the auth code is right, it seems like that would provide the same level of security as this solution.
As a side note, wouldn't someone trying to gain access to my account result in a deluge of password-link spam to my inbox? Or do they have some elegant solution for that.