Q: It appears I cannot have the TV on for my kids to play video games or watch TV while I am driving my motorhome, why is that?
A: Yes it is a “safety” feature, like you I wanted my kids to be able to play video games while driving down the road.
Our TV is in the over head area, so what I did is when generator is running(takes two people), start RV, put emergency brake on, put foot on brake, put in drive, the other person goes around and finds a working plug. The I have a heavy duty(albeit probably not needed), power strip, plug it into that working receptacle and other end gets plugged into the TV, game console, DVD player, etc.
Now some will probably say there is a way to do it with turning off a switch or something of the sorts but this was the easiest way I found to make it happen.