Windows 7: Custom Tabletop Games Console/Display Advice Needed

Hi all, i have an issue that im hoping someone may have some input for

I own a circa 1950s/60s tabletop space invaders games console, heres a pic i found of one

my machine broke when i left it turned on for a few days by accident and despite all my best attempts to fix it i regrettably had to retire it so now i have stripped out the box of everything and have an old pc and screen i plan to put inside which will load on boot a collection of classic games. Paperboy, frogger, space invaders etc
Im quite happy performing the build but the part im not sure about is that the unit has controls on both sides which i have constructed two digi to analogue joystick adapters to retain and on the original game the display would flip 180 back and forth when changing from player 1 to 2 and back something i really want to keep but i dont know how or if its even possible, if anyone has any experience of this or knows a way to do it i love to hear any advice or suggestions

All input is welcome and appreciated