3D-scatterplots are sometimes a bit confusing, especially if you can't rotate the plot around. However, the scatterplot matrix supports the interpretation, at least here, rather nicely, even if it is missing the colors.
As a.desantos already pointed out, the individual scatterplots in the second image are projections on different planes. If you think how the points in the 3D-scatterplot have to be located in order to give these projections, it maybe becomes clearer.
The projection to the plane x1, x3 would look roughly like this (can't get the image to load up, colors are marked with letters as follows: r=red, g=green, y=yellow, b=blue):
X3 |y y y y y b b b b b
|y y y y y b b b b b
|y y y y y b b b b b
|y y y y y b b b b b
|y y y y y b b b b b
|r r r r r g g g g g
|r r r r r g g g g g
|r r r r r g g g g g
|r r r r r g g g g g
|r r r r r g g g g g
+-------------------
X1