Is the app taking more than one photo? It wasn't clear in the blog post. AFAIU to have any depth perception you need to take more than one photo. Calculate the pupil distance (the distance the phone moved) then match image features between the two or more images. Calculate the amount of movement between the matching features to then calculate the depth.

As described you then map the depth into an alpha transparency and then apply the blurred image with various blur strength over the original image.

Since you're able to apply the blur after the image, it would mean the google camera always takes more than one photo.

Also a Cool feature would be to animate the transition from no blur to DOF blur as a short clip or use the depth perception to apply different effect than just blur, like selective coloring, or other filters.