Equation of state (EoS) relating volume and pressure or other thermodynamics state variables is well-established in crystalline systems, but remains rather incomplete in structurally disordered materials such as metallic glasses. Recent experiments and calculation show that the EoS in some amorphous metals exhibits constitutive behavior deviating significantly from that predicted from many well-established EoS, suggesting fundamentally different mechanisms in operation. But due to the lack of long-range order, it is difficult to uncover the underlying atomic process directly from experiment. Here we report a systematic investigation of the constitutive response of a model ZrNi metallic glass under hydrostatic compression by using extensive molecular dynamics simulation. We show that at low-pressure, the EoS is dominated by large decrease in the excess volumes, presumably those of the valence electrons; and at high-pressure, hardcore repulsion takes over. The two is bridged by a polymorphic topological transition occurring in close association with Ni, one of the alloy elements with much lower compressibility and rigid neighbor bonds that exhibit the topological transition in both short and medium-range. The complex and detailed topological rearrangement reported here may form the general underlying mechanism for the EoS of many metallic glasses composed predominately of metals with different compressibility, such as early and late transition metals and some rare-earth metals. The necessity of the electronic structural change thought to be responsible for some reported EoS is discussed also in light of this work.