When an injury occurs, one of the first things to occur is swelling. Now if this occurs say in the arm or leg, it can swell up with some room to spare except in really severe instances such as compartment syndrome. Needless to say, that is not the case for the brain. The skull is incompressible, at least when it get to adulthood. In children, infants in particular, the sutures have not fully closed, so sometimes the head can expand and change the shape of the head. Otherwise, the increased pressure by the cerebrospinal fluid and the brain can lead to dangerous increases of intracranial pressure since it can't expand.
I am surprised this person didn't develop brain herniation, which a potentially deadly complication where due to high intracranial pressure, parts of the brain are forced/squeezed across different structures. Especially deadly are uncal and tonsillar herniation, where they can cause pressure in the brain stem, the area that controls breathing and heart rate. This is especially common in traumatic brain injury, such as from car accidents, large falls, etc. Eventually if the pressure gets too high, (i.e. the intracranial pressure becomes higher than the cerebral perfusion pressure), it starts cutting off blood supply to the brain, likely leading to neurological disabilities or brain death. The brain is packed very tight in the skull with not a lot of room to spare.
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