Oh boy, now even cable manufacturers are slapping the word "gaming" on their products to make a profit...
Uh wait that's not actually it, the author just has no idea what cable you'd pull to forcibly turn a console off? Ye.. ye.. yeah I.. I.. I knew that ok?!
Ok, jokes aside he was playing on a Switch (btw why is it always a Switch in Manga these days?) and pulling the power cable off does basically nothing to your game it will simply disconnect it from the TV. The Switch will just go into handheld mode.
Oops, it's actually a PS4 he's playing on, seems like I missed how they switched to the Switch.