Turn On Machine - Make sure you have PHD Slider and an arcade token. Now go to Bar 2F. Once your there, there should be an arcade machine next to some boxes and a flag. You have to get a PHD Slider kill next to the machine. Once its on you can play the game.
Race - Now you will be teleported into a race as a RC-XD. If your playing co-op everyone will be teleported in to race. Whoever wins will get a legendary reward which has a chance to be a wonder weapon. All you have to do is follow the purple arrows that are normally on the walls.
Buy An RC-XD - This part has nothing to do with the race. Go into the arcade and find the machine that says Activision Grand Prix. now kill a zombie with dead wire next to that machine. It will turn on and you will be able to buy a RC-XD instead of having to craft one.