I don't know the full context, but I expect it means that Artemis is angry and/or pouting, and sits down forcefully with his arms crossed to show as much. "Go to the naughty step" is a version of "you're in time out" or "go to your room"--the child has misbehaved, so their punishment is to be temporarily removed from the group. It's very effective when done properly. However, assuming Artemis is a good bit older than a young child, it's a bit demeaning to suggest that he would behave that way. (I've never read Artemis Fowl, so I have no idea; just supposing.)

~Neshomeh

The grammar gets worse, trust me. Plus, Holly is aparently suffering from an octopus heart disease. I kid you not.

In later books, the relationship between Holly and Artemis improves, and she does call him "Arty" from time to time.

Still, it's a terrible fic, and whaaaaat the faires fought the Daleks? Holy...