On FE Wiki:
"As it happens, on a Round Earth you do not travel perfectly straight when traveling East or West either. Consider this thought experiment:
You are on a Round Earth standing 10 feet away from the North Pole. You are then directed to travel East and are instructed to continue to do so. What happens to your path? You end up traveling in a circle, and not in a straight line that you previously thought you would.
The exact same thing happens regardless of where are you on the Flat Earth. Your path will not be straight without you having to constantly change the direction you are traveling in reference to a compass."
Except of course, if you are over the equatorial line.
On RE you don't make any turn, you just walk straight to East.
On FE you NEED to continuously make a left turn of 0.0057°/km (0°00'20"63/km) walking East.
That is a big difference. So, the wiki is not correct and it is a misleading.
Also, even if you walk in a very straight line on RE, and even starting form the North Pole to ANY DIRECTION, you will end up in the same place you started after make a round trip around the globe. On FE you WILL end up hitting the ice wall, no matter where you start and the direction you take.