I can't open your file since you're using a plugin I don't have.
But what if you make a variable "movement" that you set to 0 when the character is supposed to be idle, 1 when he's should walk, and 2 when he should run. Have these as the conditions for your move events instead of the button clicks.
Then when you click the left button, you set the variable to 1, right click sets it to 2, and so on..
Try redownloading the file , the plugin i had was Touch2 as i want to allow Mouse clicks and touch control , not sure how to allow for running on touch tho, i was thinking with the touch2 plugin i can check if two touch points are active for running..