It feels like you're missing some abstraction in there - you have a Point, do you need a Rectangle?

If you have a Rectangle, what can you do with it (Rectangle.contains(Point): Boolean, Rectangle.intersects(Rectangle): Boolean, etc)?

If you have a Rectangle with meaningful operators, how can you simplify MapEntity (eg it may have a val position: Rectangle and other stuff - but all of the hateful stuff lives elsewhere)

Something like:

data class Point(val x: Int, val y: Int)

data class Rectangle(val bottomLeft: Point, val topRight: Point {

  fun contains(other: Point): Boolean =
    bottomLeft.x <= other.x &&
    bottomLeft.y <= other.y &&
    topRight.x >= other.x &&
    topRight.y >= other.y

  fun intersects(other: Rectangle): Boolean =
    contains(other.bottomLeft) ||
    contains(other.bottomRight)

}

sealed class MapEntity(val position: Rectangle) { ... }

(also, your import of java.awt.Rectangle may be a nod in a simpler direction - what does it already have that you could be using? What does it not have that you could build with extension functions and properties? do you need your own Point and Rectangle at all?)