Move Rush is a relatively new feature that is still in the testing phase. Only a select number of players were chosen at random to try it out. I had the feature for a few weeks when it suddenly disappeared from my game. Just a few days ago it returned for about 48 hrs and I haven't seen it since. I suspect this is normal behavior.
Indeed, only a small number of people get to experience test features and they are selected at random. Test features often disappear for a while and then return after some adjustments have been made. In my experience I also had Soda Squad for a while, dissappear and then come back recently.