How to do heterogeneous volume absorption using path tracing?
Your equation for the absorption-only model is correct: You multiply the luminance $L_x$ at the surface by the transmittance of the participating media between eye and the surface. For homogeneous media you can calculate this analytically using Beer-Lambert law:
$$L_y=L_xe^{-\mu|x-y|}$$
For heterogeneous medium you can calculate the transmittance by ray march through the medium using for example Woodcock tracking explained in the paper you referred.