cloudlessPac-Man is the Square in Flatland. The player is the Sphere from Spaceland who can see through the walls.
MrPoopyButtholeFlatlanders can only see other flatlanders in a single dimension: a line. All flatlanders would look similar, no matter what shape they were, however from different angles the line that represents them would change length with some shapes and not others. A sphere is one of the shapes where the line would stay at a constant length.