Type projection example from "Scala in Action" (chapter 8)

Type projection example from "Scala in Action" (chapter 8)

could anyone help me with below code bits from the book?
trait Mapper[F[_]] {
def fmap[A, B](xs: F[A], f: A => B): F[B]
}
def VectorMapper = new Mapper[Vector] {
def fmap[A, B](xs: Vector[A], f: A => B): Vector[B] = xs map f
}
That was simple: trait definition using higher-kinded type F[_] for usage
with any "container-like" types, then a concrete mapper for Vector.
Then goes a tricky part. Mapper for Either. I understand {type E[A] =
Either[X, A]} just as a block of code, and ({type E[A] = Either[X, A]})#E
as a projection that takes that type alias E and by that "hides" the
presence of X.
def EitherMapper[X] = new Mapper[({type E[A] = Either[X, A]})#E ] {
def fmap[A, B](r: Either[X, A], f: A => B): Either[X, B] = r match {
case Left(a) => Left(a)
case Right(a) => Right(f(a))
}
}
Questions:
Why do we need X in the def EitherMapper[X] = part?
Why author tries to "hide" presence of X (i.e. Left) by use of projection,
and does not simply specify = new Mapper[Either[X, A]]?
Thanks for details.