Andy,
WRT African big game, it's gralloched on site and then loaded, by muscle power, onto the back of the hunting car, usually a Landrover/Toyota or similar pickup and taken back to camp for cutting up and turned mostly into biltong(smoked/dried meat) which is then eaten or sold. Five or six strong chaps can get a whole Cape Buffalo(minus gralloch) into a pickup bed with a bit of ingenuity and some ropes. Four can manhandle a 1000lb Eland bull again with rope assistance. Giraffe might be a problem, though, the neck is a bit floppy and the legs get in the way. There are machetes and axes if cutting up is needed. It is surprising how much weight a toyota/'Rover pickup can take. Not having hunted Elephant or hippo, I dunno, can't answer that one.
I'm told that there is a trick, sometimes used by the old Professional Hunters, whereby if the trophy animal is found a long way from the hunting car, the PH annoys the animal sufficiently to induce it to charge and everyone runs away in the direction of the vehicle. By inducing a charge enough times, they will all eventually arrive where the hunting car is parked, the Client makes the shot and the trophy is loaded onto the truck, saving all the extra driving and walking. (Now, where's that 'falling about laughing' emoticon when you need it!)
Peter