In the sentence “les médias, chiens de garde de l’ordre établi ?”, the best translation for chiens de garde is “watchdog” which is defined by the Cambridge dictionary as

a person or organization responsible for making certain that companies obey particular standards and do not act illegally

You also suggested “chienne de garde”. It is interesting because it should only be used as an equivalent for female guard dog since its other translation would be watchbitch, which is of course offensive. However, a French feminist movement has named itself les Chiennes de garde. They are watchdogs primarily against sexist insults in the media.

“Chien de garde” (“chiens de garde” is the plural, ”chienne de garde” the feminine form) means guard dog or watchdog. A chien de garde may not only bark if there are intruders, but also attack intruders.

In French idioms, dogs usually have a negative connotation, but not systematically so. Dogs can be dirty, aggressive and stupid but can also be loyal.

To say that someone is the chien de garde of someone else means that they defend that person against attacks. It implies that the chien is under control of the person being defended and that they defend them whether they are right or wrong — a dog defends its master.

There is a history in France of calling journalists “chiens de garde” of the establishment (which is what “l’ordre établi” means), of the political and economic leaders. I think this use of the term originates with a 1997 essay “Les Nouveaux Chiens de garde” by French journalist Serge Halimi. The expression in turn echoed a 1932 essay by Paul Nizan, where the chiens de garde of capitalism were some philosophers of the time, accused of not caring about the common people and thus supporting the rich in class warfare. Halimi’s essay was made into a film of the same name, the expression only took off after that.

In English, this expression has often been translated as “guard dogs” (as in “new guard dogs of capitalism”). “Chiens de garde” a bit different from “running dogs” (a literal translation of a Chinese pejorative expression) because running dog only conveys the blind obedience aspect, whereas a chien de garde is active in defense of its master.

Note that calling someone “chien de garde” without specifying that they are guarding a particular person or group of persons could have a very different, positive connotation, comparable to the English “watchdog” — a dog who detects unwelcome events.