This is a label used in football placed on a linebacker whose objective on a given play is to get to the quarterback and tackle or disrupt his pass attempt. The play is most commonly known as a blitz, and involves one or more players behind the line of scrimmage attempting to break through and getting to the quarterback. A successful blitz requires many players, but the player doing the blitzing is known as a red dog.
The label came from sports announcer Bob Fouts, who saw a photo of his dog, an Irish Setter, a red colored dog, with his legs on the quarterback for the 49ers, whom he worked for at the time. Since the idea of a blitz is to get on top of the quarterback, Mr. Fouts thought this term would aptly apply and it has stuck ever since. It is sometimes used as a verb so that a, "blitzing linebacker," is "red-dogging."