You need to clarify which part are you objecting to.
Death penalty?
The fact that it was a public execution?
His age?
The fact that the article says he said that he was defending himself?
If your objection is on the first one, i disagree that there is anything barbaric about punishing someone with death when they have ended someone else's life unjustly. Feel free to say why you think it is barbaric though, which would give something to properly address. I however disagree with the number of things the death penalty is applied to in some countries, and think we should require more evidence than normal in order to apply the punishment.
If any of the other three options, i would understand what you said and agree to a certain extent. I agree that public executions are barbaric, for more than one reason in my view. The reason i said i would agree to an extent is regarding his age and his claim that he was defending himself. I would need more details about the issue in order to be able to condemn this.
The mere fact that he said so on its own, or the fact that he cried and begged for his life, as sad as it is doesn't come even close to say that they are barbarians. Criminals most of the time claim innocence and naturally many of them will be afraid of punishment, and particularly in this case when the punishment is death.