What was the stance of Neo-Platonic school concerning the games ?
Basically "boo, not coolo". But that needn't mean very much, Neoplatonics disapproved of pretty much anytzhing that was physically enjoyable, and munera were bound up with all kinds of visceral fun. Most people didn't take them too seriously in practical considerations.
In a way, aren't jousts descended from gladiatorial combat?
No, not really. THey don't have shared roots or similar structures. Jousting is a development of tourneys, which are basically war games for young aristocrats to refine their fighting skills in. Though they increasingly became a spectacle rather than a genuine preparation for war, they always remained a participant sport. THe people who really mattered were the peoplke on the horses. THe event was laid on for their sake.
Gladiatorial combat was never about the gladiators. They didn't get to choose whether to do it and weren't supposed to be having fun. THey existed for the sake of others - initially the Gods of the Underworld, later the spectators.
Didn't Christians just start throwing pagans in there after Constantine converted the empire to Christianity?
No, but execution by gladiatorial combat was an unusual fate anyway. Mainly, if you were going to kill someone, it would be ad bestias. Or in some inventive fashion. They did that a lot, before and after Constantine, but not usually for paganism.