Here's an
article that has a couple of numbers.
They reckon to make a runway with a diameter of about 2.2 miles and circumference of about 6.2 miles. They say it can accommodate two planes landing simultaneously, even in bad crosswinds. In good weather they say three planes could land simultaneously.
He banks the runways slightly, like an oval racing track, so the planes aren't sliding off as they constantly turn.
The space savings don't come from comparison to a single runway. Rather, as the article says "Though the circle’s circumference is roughly the length of three standard runways, it’s able to handle the traffic capacity of four. And since landing airplanes wouldn’t have to fight strong crosswinds, airlines would save on fuel, too."
If the circumference is the same as three runways, then the diameter must be roughly the same as a normal runway.
Give a man a fire, and you keep him warm for a day. SET a man on fire, and you will keep him warm for the rest of his life...