"...the effort of vomiting pressed out about half a teacupful of the brain [through the exit hole at the top of the skull], which fell upon the floor."
I had my own, albeit significantly milder, encounter with this effect. A few years ago I smashed my face into a tree on a popular trail here. The result were numerous facial fractures, broken nose, orbital blowout, and apparently a fracture between the bones in my sinus and brain cavity? I'm not sure of the specifics.
Anyway, I blew my nose in the ER to get the blood out, not knowing any better, and half my face inflated like a balloon. The nurse rapidly took the tissues away, said "don't do that", and wheeled me back for a catscan revealing I had blown air into my brain. Off to the trauma unit in an ambulance for me, in the small hospitals words: "We can't deal with this".
Here is where we get to the vomit part. I was in the back of an ambulance, which is very nauseating, and was informed no less than a dozen times to tell the nice lady with a needle if I felt nauseous. She was sitting beside me staring at me the entire time with a fully prepared needle of something that she appeared ready to stick me with at any moment. Where it was going, I do not know and didn't need to find out thankfully, but it appeared to be something that would be rapidly deployed in an unpleasant location. Apparently vomiting with any kind of facial or skull trauma is very dangerous. While I was recovering, my neurosurgeon told me that he had a classmate who smashed his face on a rock kayaking in Africa and didn't seek attention, the ending to the story was he got on an airplane and that was the end of the story, leaving me with an impression that the after effects were not positive for him.
I'm mostly recovered now but later found that vomiting, sneezing, coughing, and blowing your nose are very dangerous if you have facial or skull trauma. Some of these are obvious, but vomiting wouldn't have been on the list for me as obvious. Anyway, the lesson here is if you have facial trauma, go to the ER and be careful what you do after. In retrospect, I'm glad it happened there rather than at home, where the possibility of opening my skull to relieve pressure would've existed if I had blown enough air in through otherwise benign seeming actions.