He's talking about a circle over two miles in diameter, so over 6.3 miles long.
Meanwhile, the average commercial runway is between 1.5 and 2.5 miles long (and my understanding is that typically only the largest planes need to use more than a fraction of the runway)
So, for the "average runway length" you're talking about 85-145 degrees of curvature, and most planes won't use nearly that much, especially since they'll be able to land and take off with a headwind. Plus, most of that length will be used for accelerating or slowing down when firmly attached to the ground, which I believe is considerably less challenging than the brief window around takeoff and landing, which is where most accidents occur.
I don't imagine it will be without it's challenges, but it seems as though it's making the most dangerous part of the process considerably safer, at the expense of making the safer portion more challenging, which seems like a very reasonable trade off.
The biggest problem I see is pilot training - all existing pilots are trained on straight runways, and would likely need extensive practice to be able to land safely on a circular runway. Practice that would likely be largely wasted unless there were already a large number of airports being operated with circular runways.