So, you're gonna argue with an engineer? (my wife does all the time).
The Watt is a unit of work.
The volt is the force or EMF and the ampere is the unit of electrical current.
When the load consumes more current than the system is delivering (alternator), the battery supplies the difference. When this happens in the typical automotive electrical system, the voltage is reduced unless the alternator delivers more current (amperes) to offset the loss.
So, when the lights dim, it is due to more current (amperes) being called for than is being delivered.