We present a classical molecular-dynamics study of the collective dynamical properties of the coexisting liquid phase at equilibrium body-centered cubic (BCC) Fe crystal-melt interfaces. For the three interfacial orientations (100), (110), and (111), the collective dynamics are characterized through the calculation of the intermediate scattering functions, dynamical structure factors, and density relaxation times in a sequential local region of interest. An anisotropic speedup of the collective dynamics in all three BCC crystal-melt interfacial orientations is observed. This trend differs significantly from the previously observed slowing down of the local collective dynamics at the liquid-vapor interface [del Rio and González, Acta Mater. 198, 281 (2020)]. Examining the interfacial density relaxation times, we revisit the validity of the recently developed time-dependent Ginzburg-Landau theory for the solidification crystal-melt interface kinetic coefficients, resulting in excellent agreement with both the magnitude and the kinetic anisotropy of the crystal-melt interface kinetic coefficients measured from the non-equilibrium molecular-dynamics simulations.