Plug the height of Mount Everest, 29,029 feet into this calculator, and you get a distance to the horizon of 208.8 miles:

http://www.ringbell.co.uk/info/hdist.htm

However, the distances in the post reach ~334 miles. So it's not that simple.

You'll notice that several of the entries are between mountain peaks, which is what is really going on. If you can imagine a mountain peak that is visible beyond the horizon, the distance will be greater than the distance to the horizon.