What I’m trying to understand with these pictures above is just how the fluid flow of the original setup was defined.  The original raw water pump is, I believe visible at center and right, positioned just to the left and above the crankshaft pulley, while the aftermarket pump is belt-driven, below and to the right of the crankshaft pulley. In the center and right pictures above, there is a hose emerging from the floor molding at far lower left. This same hose, in this view, appears to enter the aftermarket pump directly.

Maybe the original raw water circuit was converted into the coolant circuit. It is designed to circulate water through the cylinders and exhaust, after all.  In that case, the aftermarket pump now takes raw water and circulates it through the aftermarket heat exchanger.  In that way, the cooling connection from the original pump through the cylinders and exhaust manifold remains undisturbed.  But then that heated water must be run through the heat exchanger, and back to the original pump. possibly including an expansion tank (did they not have one in this installation, or was it removed?). Such connections would close the new “freshwater” cooling loop.  The incoming raw water is then (after normal raw water filtering) run directly to the heat exchanger, and from there into the mixing elbow, and then out of the boat.