Comparing the transmission electron microscopy and x-ray diffraction data for a disordered graphite-like (sp(2)-bonded) carbon phase (DGCP) synthesized from fullerite C-60 at high temperatures in the pressure interval from 1.5 to 8 GPa, we show that the nanocluster structure, long-range correlations for orientation of clusters, lamellar and tweed morphology, and possible macroscopic anisotropy are intrinsic properties of the DGCP, and that they can be recognized as a signature of stresses in the parent phase at different scales from the atomic level (atomic density modulation) to the macroscopic one (non-hydrostatic pressure environment). These data indicate that the mechanism of the formation of the DGCP from large-molecule crystalline carbon material, such as C-60, is quite uncommon in the standard classification for the first-order phase transitions since it displays features typical for both diffusion and martensitic mechanisms, e.g., a strong topological rearrangement of covalent bonds and a crystallographic-like relation between crystalline parent and disordered product phases, respectively.