Why are video games under critiscisim?
Because a lot of people say too much video game playing is bad for you. And this is true. So people aren't really criticizing video games, they are trying to get people to cut back on video game time.
There are two different types of batman video games. The Arkham games and the Lego games. If your child is under 10 or so I would probably recommend the Lego games. The Arkham games are more violent. Even if your kid is under 10 they will probably be fine. A quick visit to Amazon or your local video game store could probably answer these questions.