Its not barbaric - but neither does it have anything to do with good or bad "strategic corporal-ing". Its just juvenile idiocy. It's already clear that it is a positive motivational tool for your average Snuffy "yeah, ####'em, send the bastards to hell!" However, the only effect on the bad guys would be similarly emotional - to piss'em off. Or perhaps they'll just be amused, and snicker to themselves about the stupidity of the infidel as they emplace their next IED ambush. As far as the general indig population - it only furthers their perception of our guys as ignorant westerners attacking a misunderstood aspect of the faith, rather than reaching a real solution to dealing with murderers and criminals.
I agree, this is juvenile idiocy and in a perfect world it would stop there.

However, videos of this nature can and will be used in by the enemy in their IO/PsyOp releases to continue to characterize coalition forces, especially American forces, as Christian crusaders who are targeting all Muslims and who do not respect the Muslim faith, no matter where it falls on the secular to fundamentalist spectrum.

While I do not think it will spread to the same level, I am reminded of the Enfield rifle cartridge fun the British had in India.