Okay....going back through I see a little bitty note that says: "Hydraulic system is in by-pass mode when hydraulic system no longeroperates."
So there is a bypass mode (a separate valve) that takes the place of "open center". Your function valves will still show a closed t port, but flow is being relieved. Bypass mode opens pressure to tank. When closed, it builds pressure until it reaches the relief valve setting (milliseconds). On the diagram it says :Main Hydraulic Relief valve and is in about the top middle of the manifold.
That valve would provide a flow path for the pressure to go to tank. This may be the way they use gear pumps....I've done it in sawmill hydraulics when doing it right with PComp was not an option.
When you have a need for a function and pull the lever or use the solenoid, something (electrical) operates the bypass valve at the same time it operates the function valve. It closes and builds pressure, which then is either used for work or relieved back to tank.
Any function, in addition to operating it's own valve, must close the relief valve at the same time. That's a serious level of complexity that isn't necessary with the PC pump. If you have it working correctly, then a gear pump can be used. I had not thought of doing it that way and had not noticed the note before.
I don't know how complete of a unit you are working with...if it has all the interlocks and wiring and relays to control valves simultaneously? If it is entirely complete, it appears you can have a gear pump. While pressure comp would work better, this method was their choice, probably because of the higher pump price. If it works for you, all is good.
And I'll add that when using your dump, it will have to close that relief valve also, or else it will never build pressure, it will take the path of least resistance back to tank, which will be the open relief.