There's a longer land path that starts in or near Senegal and ends in China. But they miss it because it goes near the Dead Sea, and they treat anything below sea level as water.
The one they give also crosses numerous rivers and lakes. For the strict version of the challenge where you literally can't cross water it's likely that the best solution is across Antarctica. Guaranteed by temperature to contain no water whatsoever.
In passing, https://en.wikipedia.org/wiki/Paul_Salopek is walking from Ethiopia to Tierra del Fuego, tracing the path of human migration out of Africa. Walking the coast, not a straight line.
