And the truck runs a solid piston? It has hydraulic bump stops, so I wouldn't have figured the solid piston was necessary since you don't need the shocks to totally stop up travel in the suspension. The two fluid lines to the reservoir could be just to circulate fluid in and out of the reservoir as the shock cycles for cooling. That would make sense if the check-valve looking items were actually check valves - as the shock cycles and the shaft displaces more and less fluid, the check valves could be used to force fluid flow in only one direction in and out of the reservoir, which would I guess give you more cooling since the fluid continually replaced itself.
Ivan's Toyota TT appears to have such a system. There are two extra cylinders between the shock and the real reservoir, and these extra cylinders have lots of cooling fins on them - they almost look like fins on a radiator or air conditioner condenser.
Jon