I would imagine that even if a horn broke off fighting, they would file it down to prevent an even harper-ended weapon. If these were deer, I might agree, but I am fairly sure a break that close to the skull would be immensely painful. If the animal was so picked on that both of its horns broke off, I would expect it to be removed and housed with less aggressive individuals or even separated and housed with another species eg zebras. This hasn't happened which leads me to assume that this animal was very much the aggressor or a dominant individual, given that, hornless, it is still kept successfully with the other gemsbok year-round.
