Finally, a word on the "prayers" or supplications to Allah made by the Muslim executioners in the video: these are standard and formulaic.
Although the writer is making a different point, this also implies that no faith in God is involved, no higher aspirations or spirituality. What we're seeing here is just a cult, reinforced by brainwashing and rote memorization/repetition of nonsensical rules and phrases. It's as human and mundane as Nazism (yay - I did my first reductio ad Hitlerum!). Mr Okasha (according to the article) apparently says something similar.
As GiT said above, there should be no discrimination regarding this kind of thing. Violence and murder are crimes in all civilised countries, and should be tried and punished without any reference to the reason (with the exception of self-defence) or to the perpetrator's beliefs. The law must be blind. Here's General Napier sorting out the Indians (which, it should be stressed, is something Indian leaders had attempted to do themselves, without any success):
You say that it is your custom to burn widows. Very well. We also have a custom: when men burn a woman alive, we tie a rope around their necks and we hang them. Build your funeral pyre; beside it, my carpenters will build a gallows. You may follow your custom. And then we will follow ours.
People who practice backward and barbaric customs sometimes need to be dragged kicking and screaming out of the dark ages. After a while, they usually discover it's not so bad.