From what I gather from the photos you posted above it seems to me (from what I can see) that your piece looks more like this http://i.imgur.com/CoDNGQm.jpg than this http://i.imgur.com/CoDNGQm.jpg

If I am not mistaken it does look a bit flat from the pictures. Could you elaborate to me how it is not like the first link I pasted above?

Lasers also have the ability to go at different depths. I would imagine other more specialized lasers have the ability to move the laser in a 3-dimensional space to carve out an image like the second link you provided above.

All one would need to do is provide the 3dimensional vector image to the system and it would do something as complex as the second link.

Then again that last part I am just guessing as I have not used a 3d laser (if it exists).