This is really well outside the realm of simple repair, as the video demonstrates, the machine is basically totaled. There’s no monitor! The power supply is obviously kaput! They get it working though. HAPPY END!
The repair process was involved enough that they did a separate video for fixing the board itself.
Joe’s Classic Video Games: Repairing a Completely Destroyed ATARI Centipede Arcade Game From 1980, Will It Run? (45 minutes)
How we Repair an Atari Centipede Arcade Game PCB With Minimal Test Tools – Simple Schematic Theory (49 minutes)