I think he is actually analogizing the refs to the chicken,, not the players. Refs are involved on the game (chicken is involved in the eggs, but his life isn't at stake) but have nothing riding on the outcome. The players and coaches have everything riding on it, bowls, careers, jobs, NFL, etc., like the pig has everything riding on you having bacon.
Without the context it is tough to tell, but I assume this is in reference to his tirade about the officiating against Texas.