I gave the accepted definition of willpower above. The author trying to redefine the term doesn't make it so.
It's like the author trying to say that endurance is the same as free will, because free will can dictate whether or not you train it.
There is the understanding that people are just the result of their genes and environment - this is common sense. Then there is trying to say that willpower doesn't exist at all - it does, and it's medically defined.
With that being said, conscious effort is not always required to get out of bed in the morning. What if you're stressed out for an exam and you just automatically get out of bed to study a few minutes more? What if you're fully rested or hungry, so that you've no internal debate about whether you should get up or not?