The engine on the Eindecker in Seattle looks pretty much like a Le Rhóne 9C, used e. g. on Nieuports. I have not heard of any cases of these engines being actually used during WWI on Eindeckers, so this rather looks like a builder's mistake - they simply took a rotary engine from WWI. Also notice that the propeller is pretty far from what you can see on the second photo (Garuda propeller).
Eindeckers were equipped either with Oberursel U.0 (7 cylinders, E.I) or with Oberursel U.I (9 cylinders, E.II - E.III).