Some things worth noting:

Depth of field increases as the focus point moves deeper into the frame.

Depth of field decreases as your lens length increases.

Depth of field decreases as your sensor size increases.

The A570 will have a relatively large sensor compared to a mobile phone, and your subject was very close to the lens. These things considered, the depth of field isn't impressively shallow. Reducing the sensor size to that of a phone and moving the subject further away will make shallow depth of field impossible. The portrait examples on that Google page are exactly the sort of thing that wouldn't have been possible previously.

Good points; all my shallow-depth-of-field shots seem to be close-ups.

It's not so much that a DSLR is the only way to shoot with a shallow depth of field (which can even be achieved on a phone camera if you're taking a picture of a ladybug a few inches from the lens), but that the greater the aperture and/or sensor size, the further away you can get a shallow depth of field. So on an APS-C sensor with an f/1.8 lens, you can shoot a portrait with the same level of bokeh you might only get with an extreme macro on a pocket camera, and on a full-frame sensor with an f/1.2 lens, your subject might be standing many feet away and you could still achieve the same effect.

I'm not sure if zoomed-in macroshots "count", as they naturally have a more shallow DOF. Can you achieve the same effect with portrait shots?

I'm pretty sure they definitely don't count, as DOF is a ratio of focusing distance IIRC. Also the DOF would be far more shallow with a DSLR and a fast lens in the same conditions (close focus).

Your example looks fucking delicious... (currently living abroad and missing double doubles more than ever)

animal-style, no less

upvote for recognizing double double, and expressing appropriate frustration.