Vortices in a near-2d-flow like a river will absolutely be circular, vortices need to be coherent in some plane in order to sustain themselves.
The specific circumstances here must be that that the water is on the edge of freezing during downstream flow and there is a naturally-very-long-lived vortex in one region for it to initially form the ice-disc. Must also be followed by some very-gently-bounceing-off-the-edges, and the river never getting too thin for it to get stuck.
Well, no: https://ourplnt.com/earth-smooth-billiard-ball/
The myth is springs from the fact that if you had a smooth earth with a radius of center to Mariana Trench, and another smooth earth with a radius of center to Mt. Everest, you could shrink both of them by the same factor and fall within allowed billiard ball specifications. That says nothing about smoothness, only about the allowed size of ball.
If you actually shrunk the earth we're living on, the ball would still be rejected as quite too rough.
Just kidding around really, but I have to imagine that pockets of circular water currents like this, are more common than we would think.
We just can’t easily observe the dynamics of water flow until something like this happens, where a bunch of ice builds up and makes it obvious.