How To Get Them To Drop The Game Controller Instead Of Taking It Away
I want to give you the best possible answer, but it may require more information.
Just being over-assertive isn't the best idea.
There could be other things involved causing the girl to contain herself in her games. I know I had issues that were limiting me to seclusion, and once they were gone, I could easily set down the games and be more physically interactive.
First off, how old is the child? How is her relationships with her immediate family members - mother, father, siblings? How are things for her outside the home?
I immediately sense a disreguard for her mother and maybe she should take some time to find out how her daughter is doing - show some concern - in fact, her mother should state that she wants her daughter to put the game down for a moment and come talk to her - and be genuinely concerned with her feeling like the games are all that's important - get a straight answer from her.
It may be that she's having difficulty with friends or schoolmates that makes her want to stay indoors. You can try to ask about what other kinds of activities she's interested in other than games, and why she don't try doing those things more often. Her mother can try to relate to her even, let her know that she knows it's not best to always do what you want to do all of the time, that it can be harmful not to do other activities, and that her mother suggest she find time to do other things - that she wouldn't want to take away the games and instead ask her daughter to decide, for herself, to try something else for a while, that she could always come play her games later - suggest possibly a compromise between time on her games and doing other stuff, even if mom is included. kgarcia1113 had a good suggestion about compromises.
If she seems reluctant to compromise, then her mother can play the "I could just take it away, but I'm giving you a chance to do the right thing, not many parents give their kids an option" card, and if that don't work, then put the foot down the rest of the way. If it does come to this, I suggest the child be taught some lessons in responsibility for limitations.
Again, there can be many things affecting her behavior and it would be best to try some responsible reconciliation and understanding first, otherwise her daughter will steer towards more rebelious behavior.
Educational psychology doesn't take into account real world issues involving possibly emotionally disturbed children, nor the disconnectedness that discernment can cause to have an effect on children. Like kgarcia1113 stated, things don't always work the same for different people.
I'd be willing to offer up any more advice you or anyone else may need in this situation, too.