Maxperson
Morkus from Orkus
Technically, it was "in cold blood." While there is no legal meaning of that term, the idiom means without passion; in other words, in the absence of the heat of passion. As the encounter was no longer in media res, it would be correct to say that the execution of the bouncer would have been (to use the idiom) in cold blood.
A bit of background might help as well-
As a general rule, jurisdiction split on the issue of self defense; some say that it can only be used lawfully when retreat is impossible (you have a duty to retreat before resorting to self defense, if possible), others do not require retreat (stand your ground).* However, I am unaware of any current legal code, or any provision under warfare, that permits the killing of an individual who has surrendered (who no longer poses a threat).
I will refer back to my earlier post when I say that there can always be factors that we are not aware of, but I am somewhat confused that this is still a question; absent facts that we are not privy to, executing an individual who has surrendered is not a "good" act, and is almost always evil (unless excused by Gygax-ian "KILL ORC KILL" gameplay).
*Again, simplified!
Update- saw your post- even with your added definition, it is still cold blooded. It was an act without compunction or clemency; pretty much the definition of it (I surrender! No, you die.) But you're free to disagree.
I disagree with that. The fight had ended, but was still within seconds of full combat. The passions could easily have still been flowing. I've heard about murders where an argument happened and one guy goes upstairs, gets a a gun and shoots the other. They weren't pre-meditated, but a crimes of passion because the anger and emotion was still running hot.
The battlemaster could have been calm and just offed the bouncer in cold blood, or he might have been angry and out of his mind, killing in a crime of passion.
Either way it was evil.