The folks being held in Gitmo are enemy combatants, the rules of war apply to them. The rules of war does not require due process to be carried out for those captured while fighting your army.
What about the ones who weren't fighting at the time of their capture?
As an example, 2 of the "British" detainees released in 2007 were captured when their flight from the UK landed at Banjul airport, Gambia, West Africa. They were arrested by Gambian authorities, turned over to the US, and spent 5 years in Guantanamo.
These men cannot in any sense of the word be said to have been taken on the "battlefield". They were arrested passing through immigration at an airport in West Africa. There was no fighting in progress, they didn't have any weapons, and they arrived on a commercial flight from the UK.