Thanks for the question. It reminded me that I need to do a better job of explaining the math in my next book.
Keep in mind that the Y axis in Windows graphics is inverted. Positive Y is down and negative Y is up.
A 2D vector is simply a point in 2D space (x,y).
rotatedX and rotatedY represent the X and Y axis of the entity in model space translated into world space where positive Y is down.
The following diagram shows the rotatedX and rotatedY vectors obtained from angles of 0, 90, 180 and 270 degrees.
Code:
rotatedX( 0, 1)
rotatedY(1, 0)
90


rotatedX(1, 0) 180  0 rotatedX( 1, 0)
rotatedY( 0,1)  rotatedY( 0, 1)

270
rotatedX( 0,1)
rotatedY( 1, 0)
The code in Listing 6.7(c) is calculating the screen location of the corners of the rotated box by multiplying the X,Y coordinates of each corner by rotatedX and rotatedY and then adding it to the center(X,Y) of the entity.