The widget is the 'floating action button' in Material Design parlance. You're suppose to use it in screens which have a clear 'primary' purpose. In pretty much any email application, that'd be a compose email button from an inbox (or similar) view. So I guess in that particular case, it's not so much GMail taking from Inbox, so much as both of them are showcase material design apps, and Inbox just got released 'first'.
