The focus of the animation is the CMYK model, which is a mathematical abstraction, and not the device dependency of any particular print process. I consider it helpful in the same way as the animations at the articles RGB color space and YCbCr are in explaining a 3-D volume that can be difficult to visualize from a static drawing.
 We cannot show subtractive ink colors accurately but that does not mean the article cannot have diagrams. The colors I used are the same as here and here i.e. 125 colors uniformly filling the displayable range and mapped to the CMK space. Note: this is not perfect, there is no gamma correction and linearity is assumed. If anyone likes to propose a different colour law in terms of 24-bit RGB shades, I can see about putting them in the animation.
 Just noticing that it is a spinning object tells the viewer it is something in 3-D. It helps to notice that the cube rotates about its diagonal which is the K axis. Then one understands the geometry.
 The goal is to give a qualitative visualization of how ink densities are coordinated like dimensions of a space. a) In principle three inks can define the whole gamut which is therefore a cube. The article explains that black ink is added to "save money on ink" and to address the inadequacy of affordable CMK inks in very dark tones.

I think it is a forlorn expectation that any Wikipedia diagram can provide colorimetrically accurate color swatches. It is correct to show that the CMK trio of subtractive inks work, to a good first approximation, as orthogonal variables that define a color space.

jacobolus has ideas for further geometric diagrams of the printing process that should be helpful if they are based on reliable sources. May we hear more?