It is hard to know why people of any given time act the way they do. We can really only speculate. I would argue that the Roman games were like this because A) it seems to be human nature to like to watch brutality of at least some sort and B) because they had a lower regard for human life than we now do.
It seems clear that human beings have some sort of innate desire to see violence. We still today watch boxing and mixed martial arts and, in some places, things like bullfighting or cockfighting. Blood sports just seem to be something that happen at all times and places.
Of course, their games were more brutal than ours. This probably comes from the fact that life was "cheaper" in those days. People died much more often from wars and from accidents and from diseases. There was much less of our modern idea that each individual life is precious.