Nicholas Prosper shot dead Juliana Falcon, 48, Kyle Prosper, 16, and 13-year-old Giselle Prosper at their home in Luton in September.
Prosper said: "On June 30, my sister decided to make the incorrect choices on episode one of season one of The Walking Dead games, and for that her face will be mutilated further than necessary.".
As well as admitting the three murders, he pleaded guilty to purchasing or acquiring a shotgun without a certificate, possessing a firearm with intent to endanger life and possessing an article with a blade or point.
The 19-year-old had also intended to carry out an attack at the school and a loaded shotgun with more than 30 cartridges was found in a bush after his arrest, police said.
"We are pleased that Prosper has pleaded guilty and will not put his family through the pain of a trial, and that he will soon face a significant jail sentence.".
