Dog thingys have barbs that prevent uncoupling - easy to see how lots of damage was done.
I think you are mistaken. Cats have barbs. Dogs have the end swell up like a ball and gets stuck that way. The female dog also has swelling areas that cause a stuck condition.
Something about this article seems a little odd to me. Not the part about a dog attempting to mate with something other than another dog. But the part about the “coupling”. The vomitting seems strange. Dogs bite when mating, so that is probably the reason for the bleeding and the required surgery. But something about the story makes me think it’s a hoax.
Male cats are built that way, not male dogs.