My doors are at the paint shop, but my door cards are at home w/ me. You are correct about the snap-caps go where the arrowed holes are and anything farther forward are done through the kick plate. The location you have circled, I have a finishing washer on the vinyl on the door card indicating to me the location of an oval headed screw.
Later cars do not have the kick plates, but have carpeted portion of the door card there and they simply have more snap-caps between the door and the card.