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.