I don't understand your first link - it isn't clear what it is about or if Easy Event is even shown on that site.
There is no link from the event to the programme in the widget. If you want a page of events for the programme you must create that page and and a shortcode for the events to it [easy-events p="programme_slug"]. If you want a link to a page or post about the event then you must create that page or post first then add the url with html yourself in the description for the event.
Think of a programme as nothing more than a category. It doesn't serve any other purpose. The programme slug isn't a way to get a programme page url but just a way to filter the events. The description is only shown in as a tool tip when you hover over the programme marker.
See ndar.org.uk for an example. The widget is shown on the front page, the Events page (a standard WP page) shows events for one programme and a combined list of all the five programmes. Here you can see how the widget and shortcode have been designed to work together. Any links in the widget event descriptions have been added using html in the description.
I hope this helps you understand how to use the plugin.