Because the unvaccinated don't have has many of the appropriate antibodies that those that are vaccinated do.
Less antibodies = higher likelihood your symptoms from any COVID variant will be severe enough to require you to go to the hospital.
It's not black and white, so think about the vaccine as a risk management tool. It's not a guarantee that you're not going to experience severe symptoms, but it reduces your likelihood. By not getting the vaccine, you've severely increased your likelihood of going to the hospital, and that is why a higher proportion, not number, of the unvaxxed end up in the hospital.