A walker is a classical self-propelled wave particle association moving on a fluid interface. Two walkers can interact via their waves and form orbiting bound states with quantized diameters. Here we probe the behavior of these bound states when setting the underlying bath in rotation. We show that the bound states are driven by the wave interaction between the walkers and we observe a level splitting at macroscopic scale induced by the rotation. Using the analogy between Coriolis and Lorentz forces, we show that this effect is the classical equivalent to Zeeman splitting of atomic energy levels.