In the U.S. at least, there is an assumed risk you acknowledge and consent to when you put on your professional athletic team uniform and walk onto the field. The principle of assumption of risk applies outside of sports, as well, but it is unique in sports.
A participant in an active sport breaches a legal duty of care to other participants only if the participant intentionally injures another player, engages in conduct so reckless to be totally outside the range of ordinary activity involved in the sport, or fails to use care not to increase the risk of a participant over and above those ordinarily in the sport. Knight v. Jewett, 3 Cal. 4th 296, 315-16, 320-21 (1992).
Although this doesn't speak to the Zidane incident specifically, the Zidane incident didn't end up with him simply getting a red card. He was banned for three games, too. Obviously, still not the same as if he did it to a guy on the street. The player he headbutted was punished, too, by the way.