In the South Andes western edge, a very active seismic contact, with earthquakes up to magnitude $9.5$ and ca. $4000\thinspace\textnormal{km}$ extension threatens cities and very large populations. The existence of modern seismological networks along the contact allowed the observation of unprecedented earthquake cycle characteristics, which can improve our ability to estimate earthquake hazard, a main objective of seismology. Using dimensional and similarity analysis techniques, we show precise mechanical conditions under which the earthquake generation process unfolds, and derive a set of scaling equations linking renormalized variables. Later on, we test our theoretical results using a curated earthquake point-catalog by using gridding, box-counting, statistical bootstrap and fixed-point iteration collapse techniques. We found non-trivial scaling laws valid across multiple orders of magnitude capable of describing a complex interplay between renormalized earthquake occurrence and renormalized moment release rate. We discuss finite-strain and seismic-moment release-rate conditions; declustering, foreshock, mainshock, aftershock notions; cutoff magnitudes, earthquake hazard implications and a possible large-scale tectonic energy transfer mechanism.