I know exactly what type of person this guy is. They want to be a thought leader so bad, but they have nothing truly deep or new to offer, so they half-remember stories they read on the Internet -- and that everyone else has read too, because these guys only browse the big websites like Twitter and Reddit -- and hope that the blue check will give them the attention they crave so much.
Bonus: this was a reply to the video of that guy who goes to work and back home for lunch. Congratulations on understanding narration, blue check. You are truly a god among men.
The gods didn't punish people with tartarus, which is where all the endless punishments like this or Tantalus being always hungry and thirsty while floating in a pool, but the fruit overhead moves when he reaches for it and the water dips when he tries to drink, for people that did something really wrong. Sisyphus had stolen the throne of Corinth from his brother, and would kill guests, which greatly offended Zeus. He would also tell a Potomai(river spirit) where Zeus had taken his daughter Aegina, but he gave this information as a trade for a spring, which angered Zeus more than if he had just said it. Zeus wanted him dead so he would cause no more problems, but when Thanatos came to deliver his soul to the underworld, he tricked the god into entering chains. With death captured, no one could die. This angered Ares the god of War, and he went into Corinth, freed Thanatos, and killed Sisyphus. Sisyphus had one last trick to play, though. He had told his wife not to bury or cremate him, but to just throw him into the river. When he reached the court of the underworld, he asked Persephone to allow him to briefly return to punish his wife and prepare a proper burial for himself. She agreed, but once he was out he reclaimed his body and tried to keep living. Hermes dragged him directly to Tartarus, and forced him to move the stone as punishment for trying to overcome death.
The important part that everyone forgets is that Sisyphus isn't forced to push the rock.
He wasn't killed a second time, just brought to Tartarus and balancing the rock at the top of the mountain is the stipulation for leaving. Sisyphus continues out of spite and hope, and for him giving up is resigning to a real death. Rather than being cruel labor, it's a punishment playing on his nature.