" I'm also trying to fully comprehend the apparent fact that (regardless of how the game was played on TV), a second person coming to the two remaining doors, after the original contestant switched, has only a 1 in 2 chance of guessing the car's whereabouts, while that original contestant has a 2 in 3 chance."

The second person has NO choices. One goat has been revealed, the contestant has switched doors, the person then gets the original door by default. The contestant has a 2/3 chance of getting the car, therefore the person has only a 1/3 chance of getting the car.

Conversely, if the contestant does not switch he has reduced his chance to to 1/3 by staying [see the grids]. The person, still having NO choice, gets the unpicked door. But he has the better chance of getting the car, 2/3.

It is important to realize that the second person has "no choices" no matter what the contestant does, but his chances of winning the car are totally dependent on the contestant's action.