The mother of three, resident of Swanley, Kent, spend almost all her time playing the game, in which dwarfs and giants try to conquer the world. She set aside just two hours for sleep.
The court was told that the woman played almost non-stop for six months, during which her three children, aged nine, 10 and 13, didn't have hot food to eat.
The children "drank" cold baked beans from tins because there were no spoons, The Sun reported.
"She let everything go. She bought food that didn't need cooking. She fed the children pot noodles, sandwiches, chips and pies. She was ashamed," Prosecutor Deepak Kapur is quoted as saying.
After the woman's two dogs died, their bodies were left rotting for two months in the dining room, the report published on Monday, Sep 13 said.
A neighbour who got a peek at the "appalling conditions" through a letterbox raised the alarm.
Besides banning the woman from using the internet, the court has banned her from keeping animals and directed to 75 hours unpaid work.