It's an initiative to stop game companies (EA, Ubisoft, Blizzard etc) from being able to decide if you can play a video game that you've bought. The example used is for the video game "The Crew" which was an online-only racing game. After the servers were shutdown by Ubisoft, the game that many people bought became unplayable.

What StopKillingGames wants, is that any company that publishes / develop games provide a way for people who own the game to continue playing it indefinitely. This would most likely come in the form of a game server that could be run by any owner of the game, and shouldn't be a requirement that publishers / developers run the servers forever as that would be unsustainable.