MoveTo behavior doesn't control animations.
I'm guessing your animations simply play to the end and then stop. You need to set them looping in the animation editor.
And also add another event - "MoveTo on arrived: Tiger set animation to Idle"
By the way, all "Else" blocks in your screenshot are empty and have no effect. Also the angle values look wrong to me. You might want to change your code like this:
Is in Touch (parent event)
... (sub-events)
... Angle between 45 and 135 : Move up
... Else
... Angle between 135 and 225 : Move right
... Else
... Angle between 225 and 315 : Move down
... Else : Move left