I think it is more fundamental than that. Emergence always disappears when we slice phenomena thinly. A person walking through a doorway is a very continuous phenomenon. We can see their relation to the doorway at each point. There is no abrupt change. But when we stand back and apply the criterion: "is the person through the door (y/n?)" we end up with an answer. When it is yes, we can say that the passage is an emergent effect of the motion. At one moment it wasn't there, and at another it was.