In “Mars City,” after the short cut-scene of Doctor Betruger and Swann talking, continue forward down the hallway in front of you and eventually on your right there will be a room with the word “kitchen” written on the wall. Go into this room and in the far back left corner, you will find the machine.
You will need to play this game (which is literally just punching a turkey over and over and watching it explode) for about five minutes, give or take, to reach the high score of 25000 points. You will get more points the quicker you hit the turkey.
You could always just sit in front of the machine and spam the button or while you watch TV or do something menial until you unlock this if it’s too boring for your liking or you’re impatient.