My goal is to start sharing research on gaming and children. The common argument is that gaming is bad for children in almost all ways. If you can't tell, I don't agree with that. I think gaming can have positive benefits. Not just the ones that come to mind first, like hand/eye coordination, problem solving skills, but also ones that you might not think of. Reading, for example, or even social skills. This is the OPPOSITE of the commonly cited research. If anyone has ever tried doing research on such a topic, it's not the easiest to find. So bear with me while I work on my Boolean search chops.
In the meantime, an easy test to see if your family is gaming together, or if you're just playing video games at the same time under the same roof.
For me, if you are active in your gaming together, you're doing it right. Are you showing interest in what your child is playing, and vice versa? Do you watch them while they play (note: this is different from supervising)? Do you help them when they get stuck? Do you celebrate with them on successes and help console them on failures (to help keep that ugly Anger at bay!)?
The tough part of this, as with parenting in general, is knowing at what point "help" becomes "doing it for them." Kids like playing games in different ways than adults. My son loves driving his Sparrow off cliffs and jumping off the Tower (in Destiny). So be it. That's fun for him. When he plays alone, I'll let him do what he wants. Once he's in a fireteam, though, I make it clear that now he's just one of three people working towards a common goal and he has to play that way.
The opposite of active gaming is passive. There's an easy way to describe passive gaming -- babysitting. Is the game service as a babysitter? If so, consider ways you can become more involved in your child's gaming.