Question: Even though each ball is travelling at a constant velocity, why do the dots in its trail spread out as if it were accelerating as it approaches the ground?

Answer: The ring is rotating up to meet it. While the ball itself is not accelerating, the speed at which the ball is closing on its landing point is increasing.

The place the ball will land is known. As the ball is travelling sideways, the landing position is also travelling (nearly) sideways until the ball is released. As the ball approaches its landing spot, the two are travelling perpendicularly, that is, the distance between them is closing much faster.

Picture two objects moving parallel to each other. They are getting no closer to each other.
Now picture two objects travelling at right angles to each other on a collision course. They are closing rapidly.
This is what is happening between the ball and the ball's landing point on the ring.