Mighty not included.
I ordered a glass mouthpiece which is actually not the same as this product. The product I have replaces the plastic mouthpiece of the mighty. I don't think it offers any better experience than the original mouthpiece other than the feel of plastic vs glass.
This product looks more similar to the cooling stem but the difference would be the cooling unit is still attached. I think this accessory would be incredible based on my current experiences with the accessories I have (cooling stem and glass mouthpiece). The cooling stem is a bit harsh but having the ability to have a cooling stem along with the cooling unit would generate a magnificent experience. Might be on my list to try next!