If you’re painting a line then the “finish line” is where that plane touches the ground. For other races it might be a piece of tape held at chest height — the part of the body that usually goes through the plane first.
When the competitors are bicycles then they all the same height — the middles of the front wheels are all the same height off the ground, something on the order of 400mm. The finish line is floating about a foot off the ground.
The specialist streak camera photographs objects passing through a 2D plane. Ideally you would have that plane aligned vertically so that the finish plane and the camera plane were the same.
If for some reason you couldn’t do that — let’s say the camera could only be placed a few feet in front of the finish line so as to see around an object — then you would have to arbitrarily angle the camera plane to intersect the finish plane.
The intersection of these two planes will give you the “finish line”. For a bicycle race, do you set it up so that the finish line is on the ground, or floating 400mm above the ground? If you do the latter then the projection of the camera plane into the road will indeed give a line that stops short of the finish plane, but that’s irrelevant — the actual finish line at the middle of the front wheel is in the correct place.
I think the article assumes the former when the organisers did the latter?