Understanding the ordered alignment of elongated particles in dense granular systems remains a long-standing challenge in soft matter physics and is central to many natural phenomena and technological applications. In this study, the discrete element method (DEM) is used to investigate the emergence of local orientational ordering in isotropically compressed packings of frictionless ellipses with varying aspect ratios. A cluster labeling algorithm is developed to identify orientationally ordered clusters based on contacting particle pairs, with the threshold angle determined by maximizing the correlation between cluster membership and force transmission. Despite the absence of global orientational order, the packings exhibit pronounced local alignment that can be quantitatively characterized by the identified clusters. The cluster size distributions collapse onto a universal master curve largely independent of particle aspect ratio, and a theoretical model is proposed that successfully reproduces the observed distributions. In addition, the cluster shapes exhibit fractal-like scaling with a nearly constant scaling exponent across all systems examined. These robust scaling patterns are signatures of mechanics-driven self-organization in granular systems composed of elongated particles and may serve as a foundation for future mesoscopic and continuum modeling of such materials.