What exactly happened to Aaron Eckhart's character?

From the novel, The Last Ride, it wasn't Brake who was killed this way, but the killing was in it. From page 67:

He took a deep breath and then held it and slit the stitching of green thongs; the cowhide flaps spread wide, releasing a cloud of putrid-smelling steam, and Jones gagged on it, turning away. Death, in general, had never bothered him much. But this one did.

The body was curled in a tight ball and disfigured to the point it was almost unrecognizable. Nevertheless, he knew it wasn't Lily. He picked up one side of the cowhide and rolled the corpse onto its back. Mannito. The little Mexican was naked and covered with thousands of tiny puncture holes; but those had not killed him. His death had come from the green cowhide. The fire was slowly drying it, shrinking it, until it finally crushed his ribs and suffocated him.

...

Most likely they'd ambushed him and Lily, shooting the rancher and grabbing the girl, and then, later, been surprised by Mannito. Somehow they'd caught the little Mexican alive, stripped him naked, put a rope around his chest and dragged him back and forth through the prickly pear. Afterward, with a thousand cactus thorns impaling him, they'd beaten him with clubs and then sewn him up in the hide and hung him from the oak like a giant cocoon.

In the Novel, Brake was simply shot. Another character, Mannito, comes upon the girls and their captives and is caught and tortured. When Ken Kaufman turned Thomas Eidson's book into a screenplay, it was decided that the character of Mannito was to be removed, and what happened to Mannito was instead shown as happening to the character of Brake.

The Indians used un-cured cowhide (which was 'fresh' from the animal, versus having been stretched and cured into usable fabric), sewed Mannito/Brake into it, and hung him from an oak tree over an open fire. The heat of the fire caused the hide to shrink, eventually suffocating him.

This wasn't a 'ritualistic' killing in the sense that they did it for 'Power'; it was a means to ensure that a living victim died in as long and painful a way as possible, without them having to actually stay until the (inevitable) end. Dragging the man over/through the prickly pear ensured he was too wounded to have a chance of fighting his way out of the trap.