Easter egg: Go to the menu for this episode, then click up to highlight an alien symbol on the back of the right chair, then click enter for a deleted scene of Moe getting beaten up.
Brake My Wife, Please - S14-E20
Easter egg: Go to episode menu for this episode, then click up to highlight an alien symbol on the back of the left chair, then click enter for a deleted scene.
Easter egg: Go to the menu for this episode then click up to highlight an alien symbol on the back of the right chair then click enter for a deleted scene.
Easter egg: For each episode, push the "+" sign next to the play button. After pushing this, a selection of choices will come up. Whilst you are on "Play Episode", push up. Some sort of symbol will come up on the blue or red chair shaped like >||<. Push play and a deleted scene or a behind the scenes clip will be played. Episodes: "Barting Over", "C.E.D'oh!", "Three Gays of the Condo" and "Brake My Wife, Please" will have the >||< symbol on the red chair whilst episodes: "How I Spent My Strummer Vacation", "Bart vs. Lisa vs. The Third Grade", "The Dad Who Knew Too Little", "A Star is Born-Again", "'Scuse Me Whilst I Miss The Sky", "Old Yeller-Belly" and "The Bart of War" will have the >||< symbol on the blue chair. "Treehouse of Horror XIII" will have the >||< symbol on both chairs. However, the episodes "Helter Shelter", "The Great Louse Detective", "Special Edna", "The Strong Arms of the Ma", "Pray Anything", "I'm Spelling as Fast as I Can", "Mr. Spritz Goes To Washington", "Dude, Where's My Ranch?" and "Moe Baby Blues" don't have the >||< symbol at all meaning no Easter egg for those episodes.
Answer: Willy referred to an encounter he believed he had with actual aliens, while Wiggum thought he was referring to the arcade game.