I think that the decision should be left up to the parents. There is so much inappropriate content for children to become desensitized when they are young and suggestible between racy movies with nudity, foul language, violence, offensive music, or television shows and, of course, violent video games. Many parents have a challenging time teaching their children right from wrong.
There is so much exposure to material that can negatively affect children that it is almost impossible for a parent to keep up. Shooting games are no exception. You must monitor your children to make sure that these items are not too heavily influenced them. It is also essential to limit your child's exposure to anything questionable; however, if your child has their heart set on something, the parents must consider everything and decide.
Shooting games can make kids think that guns are cool, and it is okay to use them. Sit with your child and make it clear to them that guns are not toys, and if misused, they can hurt people. If they want to play a shooting game, it should only be done under a parent's supervision and their time should be limited.