A further update released today introduces game result notifications for the non-active player/s when a game ends. So, in an automated timeout situation, both players will be notified. Otherwise, just the non-active* player is sent a notification.
A couple of further options have also been added to the My Home Notifications section, to help clear any unwanted notifications more efficiently. (Delete Unread/Delete All)
Also, an email will no longer be sent out when a draw offer is accepted. A notification will be sent instead.
In future, all unread notifications will be rolled into an daily email. This is not available yet.
* The player not making the winning / losing / resigning / draw accepting move.