It is more than the computer tech. Norad's tasking to the computer people was itself pulled from the air combat tech of the time: fast planes with very short-ranged weapons. With the threat of incoming supersonic bombers, NORAD needed to get interceptors on the tail of those bombers within, perhaps, a one-mile margin if they were to employ the missiles/gun available at the time. At supersonic speeds, and fuel reserved measured in seconds, delay or calculation error was unacceptable.

Any system of human controllers talking to human pilots would not be up to the task. Even a one-second delay would have meant a missed intercept. They needed machines to make the calculations and issue the orders. Those same machines eventually even controlled the interceptors directly, interacting with onboard radar/autopilot systems to remotely steer fighters into position.

Things would be/are very different today. Long-range air-to-air missiles/radar mean fighters do not need sub-second navigation accuracy to intercept fast targets. Air-to-air refueling also means fighters can loiter in position rather than panic-launch from the ground. Pilots today would balk at the idea of having a computerized ground controller drive "their" aircraft. It is now an unnecessary and alien concept.

Had missile and airborne radar tech advanced a little faster, maybe a little less than a decade, NORAD may not have asked for all those computers. Who knows what the world would look then like today. Get the sparrow (Aim-7) missile ready in 52 instead of 58 and maybe the computer revolution happens much more slowly.