"He cleaned the whole house, except the kitchen."
Translation:Li purigis la tutan domon, krom la kuirejo.
"Krom" is a preposition, and so is always followed by the nominative.
If it were a conjunction as well then you would be correct.
(A bit like the question of whether "He is bigger than me" is correct: it depends on whether "than" is only a conjunction, in which case it must be "than I", or whether it can also be a preposition, in which case "than me" is fine.)
In the end, it's arbitrary. "Krom la kuirejon" would make sense, and perhaps "krom" will at some point be accepted as a conjunction as well, just as "He is bigger than me" is accepted by a fair number of people, though not yet by everyone.
But at the moment, it must be "krom la kuirejo".
I have a reasonably new Dutch Esperanto studybook that says it is acceptable to use the accusative case in this way, but that it is preferred to omit it.