We set this up for Meldium a little while ago and our customers love it. We wrote up a HOWTO here: http://blog.meldium.com/home/2014/5/19/setting-up-gmail-inbo...

So thats what those are! I started noticing these buttons last week with my subscriptions. Looks like Mailchimp wrote a blog post about it too - http://blog.mailchimp.com/gmails-inbox-actions-work-with-mai...

Before you start implementing this for your own services, make sure you meet the guidelines[1] for being approved by Google. Specifically, you must have a history of sending hundreds of emails a day to gmail users.

This isn't for small projects (yet, at least).

[1] https://developers.google.com/gmail/actions/registering-with...