As Timo seems to suggest, from something like integrated WarriorCams scanning each wearer and their surroundings, resulting in data which was used to construct a lifelike 3D simulation edited into dramatic 2D footage using virtual cameras in 3D space. I would add that if the Federation Council had any doubts about the final presentation, they could always ask for raw data to help verify its authenticity.
Makes sense. We do see in TUC that the Klingons use holographic communications on a regular basis, as with Azetbur speaking with the Federation president. Such 3D communications can also be used to give the Klingons an early version of a holodeck, which ENT tells us they already have.