I ran into the same issue shortly after moving in with my (now) husband and 2 step-sons. All they wanted to do was sit and play video games and the fits got really annoying really fast. I tried numerous things and now they play outside with their friends and tend not to complain too much. My step-sons were 7 and 8 at the time and I had no experience raising kids at that age. But I managed to come up with a system that worked for me.
For every 30 minutes of video games they had to first be outdoors for 1 hour. It took a bit but it was more effective and less of a headache then taking them away all together. Also put a time limit on the TV's and computers. Now they are 11 and 12 and we don't have to fight with them or listen to crying. It worked for us, and every kid and every parent is different. But it may be worth a shot.