Looks to me like they have used a lot of different techniques, and not all of them within AE. Here's what i'd try first...although i'm only guessing .
For the camera tracking, i'd use The Foundrys CameraTracker. Then select tracked points that are connected to the object you want to stretch, and add nulls to those. Then create several layers - a clean background plate, as well as a masked foreground subject.
Using an adjustment layer i'd put a mesh warp onto the foreground subject, with the adjustment layer parented to the objects tracked nulls - so that the effect remains locked to the subject.
Then composite this lot over the clean background plate.
The bendy buildings, etc are probably done in a 3d package such as Cinema 3d, which can also work with the tracking data that you can export from AE Cameratracker.
Video Editor/Audio Mixer/ Compositor/Motion GFX/Barista
Character Options Ltd