What exactly is the event that has to occur in order for a message to be marked as viewed?

There is no out of the box mechanism to mark as viewed. You can use fields on the user entity to mark the last viewed message.

I think this is an open documentation issue.

There is an event for Rules: "Message is viewed" but it is not clear when this action is triggered. Or how it can be triggered programmatically etc...

the event is probably triggered when the message is rendered somewhere such as in views.

I am currently working on a message notification center: https://drupal.org/sandbox/baumeier.it/2078043 I have all known bugs fixed and will work on documentation and the remaining wishlist.MD entries next. There's a screencast showing the basic functionality, but it's from the earlier prototypes. The current status has more features and configuration options. Any feedback and help is appreciated. (even later when this goes into "application for full project access".

grammar correction

Have a look at my answer to "How to allow users to manage their own Message Stack messages?", which IMO is pretty close to the question here. It can be summarized like so:

1. Create a flag (using the Flag module).
2. Create a view 'Messages by user'.
3. Use Rules to flag/unflag messages.
4. Trigger the Rules Component to mark messages (using the VBO module).
5. Create notifications about Unread Messages (using the "Menu Badges" module).

Note: no custom coding involved, only using some of the commonly used contributed modules (and "Menu Badges", a hidden gem ...).