The article does not make clear: The Pan Am flight never should have been on that runway. They were told to turn down the third runway, but given that the third runway was a very sharp angle, they turned down the fourth runway.
Regardless of visual conditions I always said I was "clear of the runway" after I made my turn off. Also you clear the runway on a taxiway and not another runway. This whole damn thing was total miscommunication between the aircraft and ground control. The magic word is "cleared for takeoff." I do not think this actually happened. If those words were not transmitted, KLM was at fault.
The precision of words are of extreme importance when taking off and landing in IFR conditions!
ps
The hardest part is taxiing on the ground after you have landed in an airport you have never landed at before in poor visibility.
It wasn't that cut and dried. The tower told them to take the third taxiway. At that time, they had already passed the first taxiway, C1. They didn't know whether he was speaking in absolute or relative terms. Absolute would mean turning on C3, the third one, while relative would mean C4, the third one ahead of them. C3 would have meant a 135 degree turn for the big jet, which would have been almost impossible. C4, on the other hand, would have meant an easy 45 degree turn. It seems logical that the controller meant C4, but why he didn't specifically say C3 or C4 rather than "third" is a mystery. That is irrelevant, though, because the KLM took off without proper clearance.