"I think what he's trying to say is that the only way something could change movement (in this case, going from none to any) is when an external force is applied to the controller. Any internal forces result in the equal/opposite reaction force, equalling a net force of zero."
Yes, which is why if you put a controller on the ground and let it rumble, it doesn't move. Also, human beings are stationary at all times until they're pushed. And if you're trapped inside a cardboard box, there's no way to tip it over from the inside.
Reaction forces don't cancel out the effects of a force.
"Yes, the suitcase could lift itself as long as you were applying a force. Stop applying the force, the suitcase stops. Same with the controller. You can get forces out only by putting forces in. If you just have the controller static in space, you can't ever us the gyroscopes to generate a force. "
Just by holding the controller, you're applying a force. It's not hanging in space by itself.
All that said, I have no idea if gyroscopes could do what they're implying... it's been a long, long time since I studied mechanics. I'm sure I could figure it out if I thought about it.