From watching your videos i have 2 questions about what you are trying to achieve...
are you trying to make your little dude run no matter what while he's moving?
or are you trying to make him walk if its a short distance he has to move, and run if its a further distance?
I'd simply use a "get speed" action like lordshaggy suggested, and then use a float compare along with that which will switch between your animation states as required.
this way he'll stay in idle if the speed is 0, start to walk as the speed increases, and then run if he manages to move far enough that he ramps up to whatever speed you specify and then play his run animation
edit: looks like get speed requires a rigid body to be applied to it. if that's ok for what you need then make sure you turn off use gravity and turn up its mass so it doesnt fall over
also, the mouse pick example level usese a itween move to instead of a movetowards, which is something you might want to look into as well.