This paper certainly does not suggest that 'most' zoo animals are inbred, hybridized or diseased.
First, it concerns only 4 antelope species. Then, it claims nothing about inbreeding or hybridization. Then, its methods are not well suited to detect inbreeding or hybridization. For roan, zoo animals are from eastern population. For kudu, zoo animals are from Zambezi population. For waterbuck, both wild and zoo animals genetically do not separate into two visually recognized ellipsen and defassa subspecies. So out of 4 at least 3 are not hybridized. For eland, zoo animals are from two populations, but nothing is said that they were hybridized. There is a population of pure subspecies Cape eland at least in American zoos, by the way.