As several have alreayd posted, games are a wonderful way to engage children as long as they are still learning what they are there to learn in the first place. I agree with Lisa that parents are bringing their kids to class for a specific purpose. But I wonder what that purpose really is. I have all my students complete a registration form that includes a space for them to let me know what their learning goals are as well as a space for parents to include what is important to them regarding what their children learn. This does not mean I tailor classes to students/parents requests. I teach what I teach and if they don't like it they don't have to attend. I know that sounds bad but wait.
Any class, whether martial arts or a swimming class or a class on how to tie your shoes should provide participants an avenue to express themselves. It should teach dicipline, self-respect, tolerence, and this list could go on and on and on. While I teach Japanese martial arts and my students are learning those martial arts but with that they learn Japanese culture and more importantly they learn how to relate to others including themselves in a respectful manner. How to overcome what they didn't think they could overcome. To meet obstacales, whether in class or outside of class, with an indomitable spirit.
Whether students ever use the physical side of a martial art they will all have an opportunity to apply the spiritual side. Oh, and I even make the adults play the kids games.