If intermittently checking your inbox is a half-assed walk-run that I would make last all day, the Email Game was a decision-making sprint into a headspace where you could actually focus on what needed to get done. Just respond to your emails, one-by-one, until you’re caught up. Then, on to the next, and all the way through your inbox. Choose that last option too many times, though, and the smiley face in the other corner would get sad, mourning the productivity you’ve lost to not dealing with your inbox. You could Reply, Archive, Reply and Archive, or Skip to move to your next message. It would start with your oldest email first-full-screen, with a text box to write your response, same as any browser-based email client-but with a timer in the corner counting down every second you lingered.
