The material on WP is describing a cartoonish illustration, not making a claim about what is actually observed. Note that the cartoon is drawn from an imaginary point of view outside the universe, which isn't actually possible.
There are at least two reasons why this part of the article is misleading.
(1) Even in special relativity, length contraction isn't what we actually see in optical observations. The time for propagation of light from different parts of an object to the observer is different, so what we see is more complicated. Objects can appear elongated rather than contracted, and there can be a rotation as well.
(2) It's an oversimplification to say that distant galaxies are moving away from us at some speed.
In reality, I don't think it's feasible to detect relativistic distortions of the shape of a galaxy optically. For galaxies close enough that it makes sense to use special relativity, the velocities $\ll c$. For distant galaxies, the motion (to the extent that it makes sense to call it motion) is almost purely radial. And in any case we don't necessarily have an undistorted shape to compare with, since galaxies aren't simple geometrical shapes.