side from a possible sinister plot to silence him and keep him from testifying against others (not too likely in my opinion, but posible), I would suggest the following:
1. Status within the prison population.
2. Respect from prison guards and other inmates.
3. Publicity that comes with being the person who 'meted out justice to a sexual predator.
4. A distorted sense that maybe he was making amends for whatever crimes he committed.
5. Maybe a perverted attempt to 'earn' the love and affection of his father he may not have gotten while growing up.
Who knows what else it could be. A rational person would not commit the crimes he did that resulted in life imprisonment, but that doesn't mean guys in prison who murder sexual predators don't have reasons based on their emotional/psychological make-up.
I do suspect that the guards were not all that concerned with the 'health' of Geoghan.