It’s actually pretty hilarious. A demon lord from a parallel (medieval) universe accidentally gets stuck on modern-day Earth with one of his demon generals, and he has to learn to make a living so he gets a part-time job at a fast food restaurant (MgRonalds). They’re talking about the competing fast food restaurant that moved in next door and is stealing all the customers (Sentucky Fried Chicken). There’s also a coffee chain called Moonbucks.
The hero who nearly defeated him in battle back in their world followed the demon lord to vanquish him, but she got stuck there too and works in a call centre.
Only in The Devil is a Part-Timer! will you see Satan fight against the fallen angel Lucifer who’s willing to murder to get back into Heaven and then in another episode Satan’s worried about getting his customers to come back to MgRonalds instead of Sentucky Fried Chicken.