In metallic ferromagnets, the interaction between local magnetic moments and conduction electrons renormalizes parameters of the Landau-Lifshitz-Gilbert equation, such as the gyromagnetic ratio and the Gilbert damping, and makes them dependent on the magnetic configurations. Although the effects of the renormalization for nonchiral ferromagnets are usually minor and hardly detectable, we show that the renormalization does play a crucial role for chiral magnets. Here the renormalization is chiral, and as such we predict experimentally identifiable effects on the phenomenology of magnetization dynamics. In particular, our theory for the self-consistent magnetization dynamics of chiral magnets allows for a concise interpretation of domain-wall creep motion. We also argue that the conventional creep theory of the domain-wall motion, which assumes Markovian dynamics, needs critical reexamination since the gyromagnetic ratio makes the motion non-Markovian. The non-Markovian nature of the domain-wall dynamics is experimentally checkable by the chirality of the renormalization.