I mean, you must have entered the keys wrong. I just tested it on my end and it works. You should follow NiLuJe's suggestion and edit the settings/goodreads_*.lua file in KOReader's folder.
I'm surprised I don't see a way to mark the book as read there though... I tested whole plugin and it works as expected.
EDIT: Added some more information
https://github.com/koreader/koreader/wiki/Goodreads