Yes it is not your game animal BUT there are laws in many states relative to Recreational Trespass which does increase penalties for taking of game without permission.
For example:
Recreational Trespass
Alabama: Section 9-11-241HUNTING,TRAPPING,ETC.,OF WILD GAME DURING DAY ON LANDS OF ANOTHER WITHOUT PERMISSIONAny person who hunts, traps, captures, injures, kills, or destroys, or attempts to hunt, trap, capture, injure, kill, or destroy any wild game on the lands of another between the hours of daylight and sunset without the written permission of or accompanied by the landowner or person in possession or control of the lands shall be guilty of a misdemeanor and, upon conviction, shall be punished for the first offense by a fine of not less than one thousand dollars ($1,000), and at the discretion of the court may have all hunting license privileges revoked for up to one year from the date of conviction. Any person shall be punished for the second and each subsequent offense by a fine of not less thantwo thousand dollars ($2,000) and the revocation of all hunting license privileges for one year from the date of conviction, and shall be imprisoned in the county jail for a period notless than 10 nor more than 30 days.This section shall not apply to the members of the family, guests, servants, or agents of thelandowne
Michigan recreational trespass laws beef up the criminal trespassing penalties when the purpose of the trespass is hunting, shooting, fishing and other recreational sports. In this instance, an intruder must presume that entry is prohibited – and to do so would be trespassing – if there's a boundary fence and a minimum 50-square-inch sign posted at the property warning people to stay out. If found guilty, the trespasser faces a fine up to $500 and 90 days' jail time, rising to $750 if the trespasser kills a protected animal, game or fish. Second and subsequent violations can receive heavier fines.
So although the landowner does not "own" the game animals, the taking of game without permission can result in severe penalties.