As you purchase Easy Projects, you obtain a login name (Administrator, by default) and password. Upon entering these, you are logged in as Administrator, i.e. user with a complete set of permissions. It is quite logical indeed, as it is you who are supposed to grant other users their respective rights and permissions as users of the system.
Administrator is a global role. To give a simple analogy, Administrator relates to the whole system as Project Manager relates to his or her project.
Consequently, Administrator has no defined permissions as a member of a project. That means that as such Administrator role has no place among project roles.
However, Administrator may have any permission he needs in relation to any project, as a non-member. View it as supervisory rights, Administrator being the ultimate supervisor inside the system.