Dynamic arrest in amorphous gels has so far been ascribed to glass transition. Now, experiments reveal a hierarchical structural ordering in dilute colloidal gels driven by the local potential energy, making this type of gel distinct from amorphous glasses. Amorphous gels are formed in various soft matter and biomatter when phase separation is dynamically arrested without crystallization. The dynamic arrest in gelation has been attributed to glass transition, but a microscopic foundation is lacking. To address this issue, we experimentally study the gelation of a sticky colloid model using the single-particle-level dynamic analysis of in situ confocal microscopy observations. We show that, during gelation, individual colloids first aggregate into tetrahedra, which then grow to form poly-tetrahedral clusters. Subsequently, pentagonal bipyramids are formed as sets of five tetrahedra, and finally, these pentagonal bipyramids self-catalyse secondary growth to form medium-range amorphous order and arrest dynamics. This hierarchical ordering is primarily driven by local potential energy, not free energy. Thus, the amorphous ordering and arrest mechanism fundamentally differ between gels formed by phase separation and glasses formed homogeneously. These findings will deepen our understanding of two types of amorphous solid, namely, gel and glass.