Insane- The way the narrator says he isn't insane while he talks about the murder he committed is not normal.
Wisely, Madman, Cautiously, Triumph, The Job- The narrator does not see himself as a madman. He sees killing the old man as a job or something that needs to be done because of his evil eye. He sees that actions that he took to kill the man as wise and cautious.
chuckled at heart, black as pitch, thin ray, dull blue, chilled the very marrow in my bones- The narrator is literally chuckles while thinking of killing this man and is heard by him. This installs deep fear in the man. After an hour the man doesn't go to bed and the narrator ever so cautiously shines a thin ray in his eye and his bone marrow chilled just seeing the eye.
The style the author writes in is truly a chilling style. The words he uses are not the words of a sane man.
If you do something horrible and try to justify it, you'll end up insane.