As we have two eyes one next to the other our horizontal field of view is larger -almost 180 degrees- than the vertical -135 degrees-.
In western cultures we read from left to right and top to bottom. We need to keep a good reference of what line we are at so when we finish a line (on the right) and we go to the next one (on the left) we can do it easily.
Rather than the media I think it is about the activity we do in each media. Books are (mostly) meant to read. Monitors are used for several activities, like watching videos, games, photography, etc. When text is displayed on monitors we still have it limited at a certain width so it is confortable to read respecting the former rule (a comfortable relation between the width of the line and the size of the font). Monitors being rectangle has to do with having the availability of extra information in the field of view we have more degrees which is horizontally.
There are portrait monitors which are primarly aimed for coding.
I kept thinking about this and what puzzled me is: Why are japanese books in portrait orientation?
Books are not really in portrait orientation. If you open a book you can notice it is probably wider than taller. The thing is there are two pages. The rule of having a maximum width per line still aplies. However, the physical proportions have to do also with comfortable proportions while the book is being read. Think about a newspaper, there are several blocks of lines, similarly to pages in books. So as the lines have a maximum width, a vertical distribution permits more lines being displayed. Comming back to the japanese book, the reason behind the proportions is in between these two points.