Heres the thing with Game Wardens.....they are not the same as regular police.
All regulated game animals are considered property of the state. Game Wardens are charged with overseeing the harvesting of said game animals wherever they may be, on private or public lands, and administering the laws pertaining to harvesting those game animals. They are perfectly within their power to enter any property to ensure that game laws are being followed. Doesn't matter if you are hunting on public or private land, they can enter to see if you belong there, if you have the right licenses or permits, if any game animals in your possession are properly reported and tagged etc. Given the fact that the majority of land is privately owned, if they couldn't enter to check on hunters there would be no reason to have hunting laws and land owners could hunt whenever and where ever they pleased. This would be a disaster for wildlife populations everywhere. As for the kind of surveillance mentioned in the lawsuit above, like anything else, probable cause and / or warrants would be needed.
That quote doesn't reference anything that pertains directly to the lawsuit though, its just a generalization written by the author of the article (who just happens to work for The Institute for Justice, the organization behind the lawsuit BTW) based on the plaintiffs point of view. I'd like to see an actual statement from the defense side as to the specifics of why somebody thought that it was necessary to install cameras...chances are there is a totally different story that isn't being told here....