Noncrystalline solids can be classified into glassy and amorphous, wherein glasses and amorphous solids relax toward the supercooled liquid and crystalline states upon heating, respectively. However, the structural origin of such distinction remains unknown. Herein, based on molecular-dynamics simulations of irradiation-induced disordering of $\alpha$-quartz, we demonstrate the existence of an amorphous-to-glassy transition. We show that the transition to the glassy state originates from the appearance of structural defects within the medium-range order of the atomic network. Such defects arise from the percolation of short-range defects and kinetically prevent crystallization. Overall, this suggests that the propensity of a disordered system for crystallization is controlled by the similarity between its medium-range order and that of the isochemical crystal.