Not sure what kind of a cup they were using back then (and we all know that styrafoam is disfavored today), but the temperatures were taken from the coffee pots themselves. The drive-through kid would pour it into a cup, cap it, and either hand it over to the driver or put it in one of those 4-slot cup carriers.
The woman was elderly (not spry) and had her seatbelt on in a relatively small car with "bucket" type seats. And no cupholders in the car. Because she couldn't wriggle free, the contact lasted for longer than 2 seconds. The whole situation was like a perfect storm of bad circumstances.
As
@wspcane said, the real reason McDonald's made the coffee so hot was for drive-through customers who would have the coffee in-transit for several minutes before drinking it. If you're just sitting in the restaurant, you can always get a refill if the coffee goes cold.
Just think how much MORE drive-through business McDonald's does today vs. 1989. If they still kept the coffee THAT hot today, you'd be opening up entire burn wings in hospitals to treat drive-through injuries.