Is the dancer going clockwise or counter-clockwise?
Make sure to look long enough to get the motion to flip. For me, the default is powerfully counter-clockwise -- that's what I see first, and if I look away and look back, it returns to that -- but I can get it to go the other way if I focus. (Which, according to the article, means I'm left-brained dominant.) Here's what worked for me: try thinking about whether her extended leg is going in front of or behind her balancing one -- and then try imagine it going behind when you had been seeing it in front, and vice-versa. But my wife got it to switch by changing the way she was thinking about it from logical to holistic and back again.
Any way you look at it, it's extremely cool.