There are a few things missing.
You are not registering the location the touch ended. In the events 32 and 33 System->compare 2 values, the touch.x is the initial touch location because it is in an on touch event, not the touch end location which would be registered in the on touch end event. This is needed to define which direction the player dragged their finger.
In my example under event 2, I am storing the position from the on touch event so I can compare it with the position from the on touch end event. In event 3, I am using an on touch end event to get the direction. Because you are only allowing left and right movement, you will change that event to simply check if Touch.X (which is now the position the touch ended since we are accessing the value in the on touch end event) is greater or less than Block.X and move the piece accordingly. If Touch.X is greater, move it left. If it is less, move it right.
[Edit] I just went back and read through your original post again and realized you are not just allowing for left right movement. So, you will need to look back over event 3 and learn how sub events 4 and 7 are defining the direction.
Of course, if the above appears too difficult, you could always draw an on screen directional pad and wire each direction in the same way you wired in the keyboard.