My guess is that the Model S doesn't have a battery charge indicator, which is analogous to a gas gauge, but does have a range indicator.
It appears that it has both. The remaining charge is shown as the green portion of the battery symbol.
Range indicators are on newer cars, and tell you the number of miles you have left based on the time since your last fillup, gas left, and almost never take into account conditions like speed and stop-and-go conditions.
I haven't seen those. Not sure what the value of them would be because you drive more conservatively if you are on last drops of fuel than when you have a full tank. Range indicators are actually a liability because the car manufacturer gives you a specific promise (miles to empty) but cannot guarantee it (such as if you are approaching a mountain pass.) Gas gauge can be as accurate as they want it to be, and if it shows 2.3 gallons left then that's what is left - and you can use that fuel in any way you want.
In this case the range indicators were off a bit, as many EV owners report. It's not unique to Tesla - you can't measure the charge of a battery directly, you have to integrate incoming/outgoing currents and then use voltage under some load as a fixed reference. The reporter failed because the car's power system started dropping charge left and right from the first day. One sign of trouble was the diminished range after the second charge, at Milford - it took longer than the first one and left the car with 185 miles of range. The reporter had to cover 180 miles from that point (to Norwich and back, with no chargers in between.) This would be a no-go event for me; but what can you do if you are committed already? Do you turn around and go back because your $101,000 shiny red car can't make it from the charger to the next town and back? 80-90 miles is a laughable distance for a car; you can easily cover it even on a horse.
The car still would have made it; the range indicator was tolerable at the hotel in Groton (90 miles remaining after driving 79; off by 16 miles.) Perhaps those 90 miles could be covered with a 1 hour low voltage unplanned charge in Norwich.
But here another sign of trouble struck - the battery in the morning lost 65 miles of range, and after the failed "conditioning" attempt lost 9 more. The reporter had to cover 90 miles when the range indicator claimed only 16. This was not doable, and the reporter should have called the tow to the hotel to make his life easier. Clearly the "network" of chargers is too sparse, and the car is not sufficiently bug-free (reliable) to travel between existing chargers. The self-discharge rate is simply atrocious. The reporter haven't experienced it before because he was driving continuously. It may be a bug, something that Tesla swept under the carpet assuming that the car will be charging all night anyway. This one wasn't.