Is there a programmatical way in ActionScript (maybe by using display filters) to add the white and then dark borders around objects like at the following picture? Or has the border been added to the graphical assets already by Photoshop or similar tool?

The image above is a screenshot of the game Magic Land (c) Wooga.
Yes, you can use two GlowFilters to achieve this:
You might want to experiment with the values a bit.