Yes; I wasn’t meaning to fault Pan-Am, although I didn’t realize they were already past the first runway.
The word, “takeoff” was uttered. Since the Tenerife accident, that word is only used specifically in “cleared for takeoff” and never in any other context; “Departure” is now used.
The most unforgivable screw-up seems to be that a member of the crew of the KLM (copilot?) HEARD that the Pan Am plane was in its way and sought confirmation from the captain that the Pan Am was out of the way before proceeding. The captain sought no confirmation, instead relying entirely on his understanding that they were cleared for takeoff. Given the fact that ATC had no ground radar, that everyone was functionally blind, that planes were stacked up all over the airport, that he heard plenty of background noise and interference, that he was not at his usual airport, etc., it’s incredible to me that he didn’t double-check with anyone... even if he had plainly heard, “KLM, you are cleared for take-off.” Pan Am said they weren’t out of the way; was it so inconceivable that even ATC could have made an error?
I do think ATC made an error in not more clearly specifying the desired taxiway. (If it had been C4, however, which would have made the most sense and the surviving Pan Am pilot believes it was intended to be, Pan Am would still have been on the runway when KLM came through.) That was not the fatal mistake, however. Reviewing the transcripts from the Pan Am cockpit voice recorder, it's clear that ATC told KLM to hold pending further instructions, though KLM may not have heard it due to the heterodyne caused by a simultaneous transmission. It is clear, though, that the flight engineer heard the transmission from Pan Am about it still being on the runway because, as you correctly state, he questioned Van Zanten about it. It really is amazing how many bizarre coincidences had to come together to allow this to occur.