Don't beat yourself up too much by not seeing the exhaust flapper. There is
not one to be seen when a refrigeration unit generator is removed from refrigeration unit or is not placed in the stowed position in the refrigeration container. It has a vertical exhaust pipe that mates to the elbow on your generator, the exhaust flapper sits up top on the extended exhaust pipe
attached to the refrigeration unit and is NOT part of the generator.
So the flapper that sits up top on the refrigeration unit must have been damaged and didn't close or was somehow knocked off but you would never see that without a photo of the refrigeration unit the generator was pulled from. The only clue you missed was what you already mentioned earlier about the auction note: "Limited function check: Engine Seized". Regardless, the pictures would all look the same (no exhaust flapper to be seen) from any unit removed from a refrigeration unit.
PDF Pg # 172 in the below
linked manual describes the connection procedure of exhaust extension in the stowed position.
https://www.liberatedmanuals.com/TM-55-8145-221-14-and-P.pdf
Also, note that the generator was always run in the
208v 3 phase configuration to run the refrigeration unit. So, be sure to set the AC reconfiguration switch to the 120/240v 1 phase setting whenever you load test the unit.