A mountain might be past the "natural" horizon but emerge from beyond it. Thus, two mountains at the right distance and line of sight could easily have a longer horizion distance.
And this is indeed the case for the ones at the top of the list. The longest possible distance to horizon is a little over 330 km, but almost 40 of the items on the list have longer line of site.
In fact, it looks like every item on the list is between two points that are each farther away than the other's horizon.
That raises the question of among all places on Earth where the longest line of sight is to the horizon, which has the longest line of sight?
My guess would be Aconcagua - it's the second-most-prominent mountain in the world (after Everest), and it's close to the ocean so should have line of sight to the horizon, and the Andes are pretty much a straight line in that area (and there are no other major mountain ranges nearby), so it seems likely there wouldn't be any distant peaks that weren't hidden by closer peaks.
Mauna Kea is 4,207m above sea level and can definitely see the oceanic horizon. Mount Wilhelm (4509m) and Puncak Jaya (4884m) are the highest peaks in the central mountain range on the island of New Guinea, which makes the ocean horizon probably visible from those peaks.
Western peaks in the Andes are perhaps 150-200km from the sea. A tall peak in that portion could probably see the ocean. Chimborazo (6263m) is ~215km from the sea as the crow flies, although there is a large valley ~100m above sea level in the way.
That looks like a good place to start. It's got a 4205 m peak, which would give 231.6 km to the horizon.
Next place to look is probably at Puncak Jaya in New Guinea, which is 4884 m, giving 249.7 km to the horizon. But there is enough other land in the general vicinity of New Guinea that there could be over-the-horizon peaks visible, so it would take some work to check.
