Can I do a scrollable calendar/events listing with a Drupal module?
Yes, I believe that you can do that with the full calendar module.

In the example link you posted when you click left or right though the months an ajax request is actually happening returning the next months set of events.

The full calendar module also has ajax support.

To turn ajax on on your calendar you need to look at a setting called Use AJAX under the advanced section:



There is a similar question, AJAX in a calendar view block, which may also be of interest.