A person with absolutely no motivation can still be a soldier. A person who has never seen a day of combat in his life can still be a soldier. A person with no motivation and no experience in combat situations can still be a soldier.
Why? Because such a person can still be part of an army. This situation has arisen countless times throughout history.
If a cause and the act of fighting are not the central parts of being a soldier, how can only possessing those two traits be enough to make one a soldier?
Oh, come on. Of course rubbing it in the face of the guy you are causing to die is sadistic, as is the very fact that he enjoyed killing the guy. It is exactly the sort of thing Light Yagami does on a regular basis just so the plot can show how evil and egotistical he is.