This output is typically used as an error measure. Abaqus offers similar outputs, they are meant to evaluate extrapolation errors due to too coarse meshes. CalculiX also has ERR for that (mutually exclusive with ZZS).
However, you could use ZZS for more accurate output if you take into account the differences in how it’s calculated with neighboring elements.
Unlike Abaqus or some other solvers, CalculiX provides only nodal averaged stress in .frd contour map results. However, you can use element history output (*EL PRINT) to print the integration point stresses from the seleted elements to .dat file (displayed in tabular form in PrePoMax too). There’s also this script: Stresses at the integration points in ParaView - #2 by mkraska
Yes, I think that it would be better to ask on the CalculiX forum: https://calculix.discourse.group/
Check this thread too: Zienkiewicz-Zhu superconvergent patch recovery (SPR) of stress - CalculiX (official versions are on www.calculix.de, the official GitHub repository is at https://github.com/Dhondtguido/CalculiX).