craftsman model# 917.271.022 Serial# 111698C019769 brake assembly looks incomplete

There's nothing circular in there.  
 
You are correct about the disc.  There should be one pad (very small) and the two pins
usually rust up in there so that has to be removed and cleaned.  Re-grease pins to slow corrosion.
 
Now, that main arm, (about 1" wide) is not flat and is "tappered in" on opposite sides down at the 
mounting hole.  When the brake is applied, the arm moves, the tappered in part pushes in on the pins.
The pins then push in on the pad, then the disc.  
 
 The nut holding the plate on is also the adjuster.  Tighten in the nut, the brakes are tighter.
You want a happy medium where you can apply the brake and the manual "lock" will apply and stay.
If too tight, the brake will work but will not allow you to lock it on..
 
Pull the arm and aluminum assembly off. Clean the corrosion off real good, wire wheel or sand off
all corrosion off the arm..
 
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Part #59 is apparently your brake rotor.  This, looking at the parts diagram, seems to be under that yoke sticking out (picture sucks):
https://www.ereplacementparts.com/craftsman-917271141-lawn-tractor-parts-c-158286_174089_461578.html 
 
I've never seen this design before, so maybe a shop manual would help, or just go slow
and take that yoke off to access everything..
 
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