Yeah, I really like that. I hate the way the kindle software just scrolls everything sideways. Google Play even included an option to make their program scroll like that. WHY!?
To me it always just looked like a texture mapped model. I'm looking at it again now. It looks like they replace the display with a model texture mapped with 4 pages for the duration of the animation, and they play through the frames until you let go. You are even able to scrub back and forth through the animation. There is a slight shadow under the turning page as well.
1) User touches screen in a region where page can be turned (excluding the extreme top and bottom, for toggling options)
2) Create texture map(s) of the current visible page(s), and the page(s) that will be visible after the page flips. These change depending on the display option and orientation of the device. You are either looking at 1 page or 2.
3) Draw the model, and flip through the frames of animation depending on user's finger motion. eg, at 50% through, have the page at 50% of the way turned.
4) When the page is fully turned, or the user lets go (where you play back the animation, so the page drops back into place), resume normal text display.
It could be done other ways. The text stays razor sharp with barely any distortion at any resolution. I can't say for sure if they are just drawing it real time with a distortion filter or not. There are many old flag wave and sine wave effects that could be modified to achieve this.