My guess is that they are optimizing for smartphone use cases: ie record a quick video instead of stitching together photos from lots of different folks. Using linear video as an input means you have knowledge you didn't have before: successive shots must be taken from a relatively close position and direction.

The technology is clearly deeply related to the more freeform movement variants of the past. It's likely that even better freeform movement can be stitched together from a collection of linear videos than could be from a collection of stills in the past. I wouldn't be surprised if we see that start to happen soon.

This isn't really about 3D reconstruction (there exists better solutions for that already, see http://vimeo.com/61625715) rather it seems that it's more about stitching consecutive photos together. If you press C in the demo you'll see that it appears to create different 3D geometry for every photo. This approach allows movement in the scene.

They have translation and rotation. What path can you not construct from those?

It's my understanding that you can't use them simultaneously. You have to choose one of the types: spin, panorama, walk, or wall. (http://photosynth.net/preview/about)

In the previous version, random pictures around a scene could be stitched together allowing an experience you could explore. For example, one of the original, popular photosynths allowed you to explore inside an art studio. You could look up at the ceiling, walk on various paths, move close into pictures, etc. In this new version, you're stuck on rails.

tl;dr: In this version each node has two exit points: next or previous picture. In the previous version each node had an unlimited number of exit points to other pictures.

Note you can press "c" to make the camera break free of the rails

Thanks for the tip! But this allows you to move your perspective outside of the rail system, but doesn't change the fact that you only have images established on the rail system itself.