Murder is the unlawful killing of another person with intent (usually "malice aforethought", but in some cases intent is shown through other means, as in felony murder statutes).

Killings committed in war against enemy combatants are, strictly speaking, not murder.

They are conditioned to kill the enemy without thinking, however, so I agree with you that far, and part of the process of making sure that soldiers can kill the enemy when necessary inevitably involves a dehumanization in their minds of that enemy. I wouldn't be surprised to find out that this happens ALL THE TIME in virtually EVERY war. We know that irregulars frequently go farther than that, mutilating corpses (such as chopping off genitalia and shoving it down the corpse's throat). Obviously, from a public relations perspective the army should avoid that sort of mutilation (unless they burn the bodies, which would be a good policy), but the real thing that was stupid here was to film it and distribute that video.