I'm an anarchist, but I would object to calling Chris Kyle a murderer unless he killed non-combatants or those engaged in combat specifically to defend private property and civilian lives from the US invasion. If he only killed Iraqi soldiers defending the Ba'athist regime, then his killings were morally neutral in my eyes, like killing someone in a consensual dual. It's nearly impossible to engage in state-sponsored warfare without trespassing and destroying private property, so he is almost certainly a criminal to some extent (and definitely a tax-feeder), but he isn't necessarily a murderer.
Does anyone know any details about who he killed?