"The U.S.-South Korea status of forces agreement allows servicemembers to be turned over to South Korean custody if servicemembers are suspected of heinous crimes and law enforcement officials request it" (http://1.usa.gov/yrzicW)
I don't know what status of forces agreement exists in Afghanistan.
There is no legal mechanism to turn him over to the afghanis. (Any legal war specialist, please correct me if I am wrong)
http://www.washingtonpost.com/world/asia_pacific/american-so...
Although as far as I am aware, the Hague has ultimately very few legal powers anyway unless the US refuses point-blank to investigate or voluntarily hands over the investigation to them.
edit: just trying to add a bit of clarity. whenever people use new words to describe well-known phenomena, they're simply deceiving themselves until old lessons are relearned.
'The Great Game' would probably be the classic euphemism for the ongoing Afghani affair, since that is what it has been called since the days of Rudyard Kipling.