@alma, since this story is from gutter press whose reports are just sensational journalism, my feeling is that what you see is not what was the reality on the ground... Allow me to expound
First, I've said again and again that it is not a Muslim who does not follow Islam, whether he calls himself a Muslim or not. So please do not blindly say "These muslims are just pathetic."
Secondly, Islamic law is not applied blindly. Not that somebody accusing somebody of killing a baby and law is just applied like that, no. Islamic law requires that there be four witnesses for the application of this law, Reliable witnesses, not just anybody, but people who are known to be just and righteous. And without those four witnesses, the law cannot be applied.
Thirdly, now regarding this case, coming from gutter press, they report that it's the father of the dead baby who is executing the woman. I doubt that. My suspicion is that, this is death sentence issued by the court and evidence and witnesses verified. And the one meting out the justice is the state's judicial executioner.
Fiftly, if the above was death sentence, carried out by state's judicial executioner, then note that these laws are applied and done publicly. People should be present to observe it. It is not for entertainment in public, but for them to see law and its application. The sight of it helps to enforce in the minds of the people that the laws are being applied and we should avoid these kinds of crimes.
IMPORTANT: I'm not supporting or CONDONING sporadic killing by anyone against anyone. NO MATTER where it is: Saudia, Iraq, Afghanistan, Pakistan, or U.S, or France, or ANYWHERE... Islam is AGAINST killing. YES! the victims maybe perceived as evil doer, anyone may disagree with them. BUT! We are not allowed to go out and kill them.
NOTE: My response above is informed by the fact that this news are coming from sensational journalism, which should be consumed with pinch of salt.