Bender calls the store owner Squidward Scissorhands, a cross reference between the SpongeBob SquarePants character of the same name and Edward Scissorhands.
The episode's title is a reference to 20th Century Fox, which produces Futurama and The Simpsons aswell as the fact that Futurama is currently set in the 31st century.
During a scene the Hunt Master says, "We are hunting the most dangerous game," a reference to the short story The Most Dangerous Game by Richard Connell.
The episode may also be a reference to Resident Evil 4's first chapters, where a forest is littered with trip wires and bear traps. After Bender rescues a fox, it comes back to aid him during peril much like Leon does with a dog. Though this may simply be mere coincidence, the dogs use the same sound effects in the game itself, especially during the scenes where they hunt Bender.