When we use barre chords instead of open, yes, the relative chord shapes will look the same - or certainly can.
Here, the simpler open chords are shown, using open strings where possible, so the shapes are dictated by that restriction.
For example, each root chord here shown has a different shape, C A G E and D, so it would follow that the other chords, say, V, would all suffer the same fate and all have a different shape too.
Once you progress to barre chords, and find a set of seven, then moving them all up by the same number of frets , with the same shape for each ii, iii, IV etc. will incorporate the same shapes, just moved up. This cannot happen with different start shapes, as the open chords dictate.