Justifying the beheading done there is just evil. By Sharia if you're just an apostate or kafir paying jijiya who has done some miniscule mistake which might include affecting the feeling of an Imandar(i.e Muslims). Now anyone can be a kafir because the definition of being a muslim is extremely vague in Quran and hadiths, so that's why you see violence between shia, sunni, ahmediya and all others. Even different factions between Sunnis.

I'm not defending capital punishment in the Middle East, but pushing against the "culturally dependent beheading" quip.

how?

The electric chair and lethal injection have both resulted in torturous, prolonged deaths for some victims. If beheading is done correctly, you essentially die right away.

I would argue that the masses of people that flock to see the beheading also result in some stress towards the victim. But the fact that it is not a clean room beheading but a public one culturally dependent too ...

If we argue which type of death is more or less pleasant we've directly descended into not just the Middle East, but the Middle Ages.