I disagree that the post argues that the interfaces are particularly "unnatural" -- as far as I can tell, it is about the visions of interfaces reaching much less far than the author thinks they could.
All of the squeeze gestures I know of are based on a simple and (in my opinion) natural principle: if you touch a spot and move your finger, the spot moves along. This is true for dragging, rotating, and for both kinds of resizing (zooming in and zooming out). With a third finger, one could keep two fingers in place and then skew the image with the third. Alternatively, if the image was 3D, it could be a rotation. I just came up with these interpretations a minute ago, but they're not anything new; they're just a natural extension of the same principle.
What the article does say is that limiting everything to this one principle is very limiting. Nobody ever holds their phone in the scissor grip because it wouldn't be any use. What if phone designers created a use for that? The Wii was a step forward in this regard -- you could do all kinds of things with your body and control games that way.
To give a further example of what we could have with the current "vision" versus a more future-oriented vision: let's say you have a graph and you'd like to manipulate the nodes and edges. The current vision could give you a flat table with the graph projected on it and let you touch a node and move it, or touch the side of a node and drag a new edge to another node. Another vision could give you a pit of sand and let you places smooth stones on it for nodes and run lines through the sand for edges. If I understand the article correctly, that's the kind of difference it's looking at, and I have to agree the first is a little underwhelming.