I haven't looked at the Doarama's code, but observing the movement it seems to do something like this:
The farther away a property value is from it's target value the faster the camera travels to this target value.
There's a target range that you can alter with mouse-wheel.
Target heading is the heading from camera to entity.
Target pitch seems to be somewhere in the neighborhood of say -10 to -30 degrees pitch.
Also when paused it slowly rotates the camera around the surface normal at the entity to keep it lively.
I believe it is custom tracking code not part of Cesium, probably executed via .onTick or .preRender.
The info window is quite sophisticated as well; you can drag it around via the title bar or resize it by dragging a side or a corner, and click the photo to swap (3d to small window, photo to large window.)