On the largest map size in the last game to have squares at all (Civ 4), about 278km east-west if you assume that the cylindrical map has the same circumference as earth does at the equator. Smaller if you assume that the the map has the same surface area as the Earth instead of the same circumference. (The answer you linked is based on the hexes of a later civ game, but based on Earth’s land area.)
Later Civ games the answers are larger, since, as well as switching to hexes, the largest map size is smaller in each subsequent Civ iteration (5 is smaller than 4, 6 smaller than 5, and 7 uses the same sizes as 6 but cuts off the two largest.)