We Exist in 2 Worlds at Any Given Moment
The chess game represents the outer world because it requires multiple players who all have to abide by the same rules no matter what they believe in. Much of the experience is determined by how skilled you are at playing the game, and how well you interact with other players.
The dream catcher represents the inner world because it requires a belief system to have any value. It has no physical use in the external world. The dream catcher becomes meaningful when we understand what it is. When we believe in it, we allow it to enter our inner world and function as a reminder of the importance of dream recall.
There is a lot of overlapping between the inner world and the outer world where both worlds are aligned. But there are also parts of our experiences that only exist in one or the other world. For Example our physical organs only function in the outer world, while our dreams can only be experience in the inner world. This makes dreaming vitally important for our journey through life.