1. They stared fighting after having an argument. Both were armed. You are just showing a vision from the movie, which is not the case.
2. the only KNOWN example of large scale executions is actually Agincourt. The other prominent figure murdered after being captured was Earwig , elder half-brother of king Edward the Confessor and claimant to the English throne. These things happened but on Kingship level. In feudal times, your king was the law, you were just a vassal. If you wanted to eliminate someone, you would keep then in the tower for decades (like Charles of Orleans),coerce them into singining treaties and then ransom afterwards (like Charles the Blois or John II of France). Please give me actual examples of nobles executing other nobles on a whim (and other than Agincourt). In almost ALL cases, there would ransoms. Nobles that couldn't pay their own ransom? Highly unlikely. Noble Knights were middle ages equivalents of millionaires or even billionaires my friend.