Initially after reading your question I thought that it was using the stiffness method but after seeing the image on page 7 of that forum post I don't think that's what it is. This is because the stiffness method relates forces to displacement using the members' stiffness properties. I don't see any of that discussed on the forum.
Instead, it just seems like a force balance in each of the XYZ axes and a moment balance about each of the XYZ axes giving rise to 6 equations. Depending on how your 3D truss is supported you may have 6 or more unknowns. Using matrices is just an efficient way to solve many simultaneous equations. I'm not sure there's a specific name for this given the context of your application. In terms of mathematics it is just linear algebra (i.e. solving a system of linear equations).
Perhaps with more information about what you're trying to achieve (maybe a diagram of your suspension system) we can better guide you. The assembly can be modeled as a 3D Truss like you've stated. Normally you would come up with a Free Body Diagram (FBD) to figure out how the 3D Truss is supported and loaded. From there you would solve for the reaction forces where it is supported. This looks like where the 6x6 matrix comes into play - you'd use that to solve for the reaction forces of the suspension system on the chassis. Then you could use this to find the internal forces of the suspension members if that's what your ultimate goal is.