Perhaps not, but I l also wouldn't call it "good" or even "not evil".
If I'm playing a game in a more modern setting and my character walks into a bank and the guard decides I look suspicious and draws his gun on me then rethinks and decides to put it back in his holster would it be not evil for my character to draw and put him down because "he drew first"?
If my character is in a saloon and brawl breaks out and the saloon owner pulls his trusty double barreled shotgun from below the bar and levels it at us and tells us to knock it off and after we've settled down and the owner puts her gun away again would it be not evil for my character to shoot her because "she drew first"?
Good characters don't get a free pass to do evil because someone else started it, or because their blood was up or because they we're drunk etc. etc. etc. That's what sets good characters apart.
Based on the orignal post I would call these incorrect analogies.
Closer analogy: you walk into a bank and the bank guard thinks you look suspicious and OPENS FIRE because you got in a shoving match with another patron. The saloon owner stops a fight between two fighters by OPENING up on the fighters with BOTH BARRELS. In the story the bartender wasn't just waving the steel around as a warning - he tried to do bodily harm (and may have drawn blood, the story isn't clear on that point, just that he sucked compared to the battlemaster). If you have a concealed carry permit, and lawfully have the firearm, the line is a little grayer. It's not outright cold-blooded murder, though depending on circumstances it may be manslaughter. In D&D terms, it's not good, but it's not outright evil, either.
However, game system REALLY matters here, because this is 5e - a combatant can easily put someone down at zero hit points and choose not to kill them. In 3e, there is no easy nonlethal coup de grace, not everyone carries a sap at all times, and is very likely to fail at their weak coup de grace because they're not rogues. If anything might argue it being an evil act, it's the battlemaster not taking the advantage to just smack the bartender on the back on the head with his sword hilt instead of running him through.
An alternate scenario: in the middle of a battle, a warrior draws steel and means to do obvious bodily harm to a physically weak cleric and his fighter buddy. The cleric catches him with a hold person, and the fighter takes the opportunity to run the warrior through. Is it an evil act? He is helpless - yet had he made his save, the cleric would likely have been slaughtered.
What if the warrior is the only combatant, and a sworn enemy? Is it still evil to slay him, or is it self defense?