The primary authority for the principle that hunting is a privilege and not a right is in caselaw. State v. Tice, 69 Wash. 403 (1912), is the main case. It’s old, but still good law. Below is a quote from the case:
"The decisions of the courts in this country so far as they have come to our notice are all in unison in holding that there is no private right in the citizen to take fish or game except as such right is either expressly or inferentially given by the state. In State v. Snowman, 94 Me. 99, 46 Atl. 815, 50 L. R. A. 554, 80 Am. St. Rep. 380, the court said: ‘The fish in the waters of the state, and the game in its forests, belong to the people of the state, in their sovereign capacity, who, through their representatives, the Legislature, have sole control thereof, and may permit or prohibit their taking.’ In Smith v. State, 155 Ind. 611, 58 N. E. 1044, 51 L. R. A. 404, the court said: ‘The individual has no natural right to take game, or to acquire property in it, and all the right he possesses or can possess in this respect is granted him by the state.’ In Ex parte Maier, 103 Cal. 476, 37 Pac. 402, 42 Am. St. Rep. 129, this view is expressed in equally strong language as follows: ‘The wild game within a state belongs to the people in their collective, sovereign capacity; it is not the subject of private ownership, except in so far as the people may elect to make it so; and they may, if they see fit, absolutely prohibit the taking of it, or any traffic or commerce in it, if deemed necessary for its protection or preservation, or the public good".