Look at the source to see how the corridors are drawn from back to front. This is an example of the use of Painter's Algorithm. It's simpler than raycasting, but a little more expensive in CPU terms, but as long as it redraws fast enough, does that matter nowadays? A small amount of shading is applied as a depth cue.
See discussion at http://scratch.mit.edu/discuss/topic/50892/ It should be possible to tweak this code to allow you to move through the maze smoothly rather than jumping to the next maze square, since the drawing is done one x pixel at a time. (An alternative rendering scheme is demoed at http://scratch.mit.edu/projects/31586220/ which stamps each level of the corridor with a scaled sprite)
