Shadow Moon is technically not a god. He could be considered a demi good, if this was set in a Rick Riordan novel and he would technically be, Percy Jackson. However, he is Mr. Wednesday’s, otherwise known as Odin, son and that of a mortal woman.
There are distinct differences between the Neil Gaiman novels and the Starz series due to different aspects displayed by each. The plot does try to keep to the original. Moreover, the two do not derail from what Shadow Moon really is.
Shadow moon is depicted in a variety of ways as a cross over between two worlds, the old gods and the new gods, life and death, the gods and the mortals etc. This could be why he was picked by Odin or it could also be the fact that he is Odin’s son.
The reasons behind that lies solely to the understanding of the reader or the viewer. American gods is a show that has time and again proven what a plot twist stricken land mine it can be. It has left fans wanting and guessing through its two successful seasons and asking even more questions regarding it.