Yeah, it's a bit sensationalist. By that logic you could argue that writing on a piece of paper is 4-D: horizontal and vertical position, what letter/symbol is there, and color. You could add font and underlines/italics to encode even more data per symbol if you wanted.
Well yea because a dimension is infinitely divisiable.
so a dimension can hold infinite dimensions within it.
like i.e numbers.
Orientation is at least 2 dimensions (see e.g. spherical coordinates).
Orientation of a vector is 2 dimensions (spherical coordinates), orientation of a 3D object is 3 dimensions (Euler angles). It all boils down to the fact that you can rotate the vector using itself as its axis and it stays the same, but you can't do that with, say, a cube.
Hence I said "at least" :)
In the image of the data being read it looks like the laser only hits the structures from one direction. I think the "orientation" parameter is actually the polarization angle for the ray, so only one dimension.
Could be true, but then those spatial dimensions should probably be 2 instead of 3 (laser coming from one direction means you lose that direction).