Actually yeah, that's exactly what happened. Superman pretty much just knocks Doomsday into a coma and "dies" in the process. You find out like the Very next issue that Doomsday is still alive.
I am not sure how well you know superman but he has killed multiple times throughout his history. He has killed sun eaters, humans, the anti-monitor, darkseid's para demons and he even killed Zod before.
In the cartoons, a superman from another dimension killed lex. He even killed green arrow and Wonder Woman in a what-if comic which isn't canon but it helps to set the precedent of him killing.
You can stop bullets and bombs but your spine is weak as a human.

I felt his pain when superman killed those embryos. Faora was
her and the 11 ft. Goon were like the super Chris and Snoop. Zod didn't even want beef with Jor El.

