The Romans eventually outlawed human sacrifice to the gods, but gladiator games were practiced until the Roman Empire became Christian. How did the Romans consider the gladiator games different?
TL;DR: Most of the people that died during the games were not gladiator fighters, the types we most commonly see in the pictures or representations, but were people sentenced to death.
To understand why the gladiator games were widely practiced and were seen like normal, we must first differentiate the people that participated in such games. We find four main categories of fighters: noxii, damnatii, ad ludum and auctocrati
noxii: Composed mostly by prisoners of war considered not suitable for fighting. They were used mostly in recreation of Roman battles (on the side that lost) or for "fighting" in bestiarii games (with wild animals) in particular in damnatio ad bestias (games were all the people were supposed to be killed by the animals with no survivors).
damnati: They participated in the same games like the noxii, but they were composed of slaves (instead of prisoners of war) sentenced to death.
ad ludum: These were criminals sentenced to death. They were lucky in participating to the games because they could potentially win their freedom if they were successful enough as a gladiator (an opportunity not given to the noxii or damnatii). Otherwise they died like sentenced in the first place.
auctocrati: These were initially free man who accepted the life of a gladiator as paid volunteers. They were the best trained and best equipped fighters of the arena and never participated in slaughtering games (unless they were the slaughterers).
For the most part the games were organized in fights between the well trained and well equipped auctocrati versus the other types of fighters, resulting most of the time in the death of a person already sentenced to death by the Roman law.
Fights between auctocrati were common as well, but were more like technical fighting, most of the time without death or serious injuries. Under Augustus' rule, the demand for gladiators began to exceed supply, and matches sine missione (death match) were officially banned.