Ohh, I liked this. Very in character, very easy to read (you can just hear his voice in your head as you read, you know?), very enjoyable. I'm favouriting this.

The name Gladstone sounds horribly familiar.

Thanks for this great read. It's quite a good rendition of the killing moment. I like the puzzle comparison a lot. Some suggestions (by no means exhaustive) follow:

-Typo in paragraph 3
-"The secret that pains me, that inflicts pain." -- I understand from this that the secret hurts both Dexter and his victims, but this is can be made more clear.
-"I tease the dark passenger inside" -- "inside" is redundant.
-"in the darkness of my soul" -- rather clichéed
-"But I don’t want to stay. The Code, the secret, is telling me to leave this place and never return." -- does he not want to stay because of his own reasons, or because of the Code?

Hope that helps :-)