I’m measuring the distance by line of sight, not by the distance along the surface. How far you can see is not the same as arc length - it’s a straight line.

I understand how you are measuring the distance. It's your problem and you can do it any way you wish. I am just pointing out that the standard way to measure the distance between two points on earth is along an arc on the surface between them. If the earth were a perfect sphere these arcs would be on great circles. And, as you have noticed, for your particular calculation it doesn't make much difference.