Eh, afraid he's correct there. Just think about that rationally. Yeah, they had lots of fodder, but properly trained Gladiators weren't cheap to eh... train. It didn't make sense to have them kill each other quickly.
That said, of course there were plenty of deaths (mostly convicted criminals, not trained Gladiators) and also some deathmatches between Gladiators now and then - a
high point of entertainment back then, which is why you see those deathmatches depicted in movies almost exclusively.
And
that said, I loved the over-the-top gore in Shadow of Rome's arena sequences.