That is some odd stuff there. It would seem they wanted relief valves on the dry pipe to the cylinders. Perhaps there weren't any on the cylinders. Did they put new piston valve cylinders on the engine or does it still have slide valves?
The small cylinder suggests they wanted to be able to close the relief valves at will. The plumbing of the air pump exhaust into the dry pipe
Was probably done a to put steam into the cylinders and valves while drifting without opening the main throttle - which would admit superheated steam into cylinders. The check valve kept superheated steam from going back through the pump exhaust to the air compressor.
The Greenbrier, Cheat & Elk (West Virginia Pulp & Paper Co, later Mower Lumber Co. - the guys who ran the RR at Cass, WV) did something sort of similar with their big #12 at 150 class 3 truck (later turned into a 4 truck monster). In this case they plumbed the air pump exhaust into the dry pipe going to the cylinders (only one pipe on a Shay) and controlled the admission of the steam with a 3-way valve and a long operating rod running back to the cab. Again, the idea was to put wet steam into the valves and cylinders the get oil to the valves and pistons when drifting down hill. In this case, it was a superheated engine with slide valves, which is not a good combination. Lima a claimed it was no issue with Shays, but a good many of the large 90 tonners were re-fitted with aftermarket piston valve conversions.