Granddaddy becomes involved in the story's conflict because Granny asks him to. Because she hasn't been successful in getting the men off their property, Granny decides to enlist Granddaddy Cain's help. One of the children, Cathy, feels that Granddaddy's tall stature and kingly demeanor make him stand out. People are naturally drawn to him.
Essentially, Granddaddy's success in handling the conflict is due to his formidable nature: he expects his desires to be respected and acts accordingly. Granddaddy Cain acts as if he has the authority to order the men off the land, and he backs up that authority with his actions.
When the hawk's mate attacks everyone in its grief, Granddaddy Cain simply fells the bird with a well-aimed throw of his hammer. The hammer brings the hawk's mate down. What this does is demonstrate to the trespassers that Granddaddy Cain will do whatever it takes to protect his property and his family. Furthermore, it's just plain unnerving to engage in conflict with a man who has such impeccable aim.
So, the men hand over their camera to Granddaddy Cain because they are afraid of him. If the accuracy of his aim is anything to go by, Granddaddy Cain isn't the kind of man who tolerates fools gladly. So, the men barely manage a weak protest after Granddaddy Cain destroys their camera. They then take their leave because they are too afraid to stay to demand restitution for their loss. In the end, Granddaddy succeeds in reclaiming the upper hand after demonstrating that he will do whatever is necessary to defend his family and property.