The Game: 'One Chance' by AwkardSilenceGames
Okay, this isn't actually mindless. Okay, actually, it's the opposite of mindless. It asks you, via crudely pixellated characters and limited controls, to make life and death decisions that reflect your deepest values. But I'm the kind of person who makes life and death decisions without really thinking about them. In fact, I played the game while doing two other things at the same time, which is probably why I ended up dead in a park with the ruins of creation turning to ashes around me.
The Scenario: You're a scientist who is responsible for an experiment which, unfortunately, will destroy life on earth in six days. Every day, you're asked to make choices about what to do. Do you work to try to stop the destruction? Spend precious time with your family? Hook up with a willing co-worker, because, well, who needs a because? I am told that the choices you make actually affect the outcome of the game -- this isn't a sick joke -- but be aware, the designer is serious about the One Chance thing. You get to play it once. Try to play it again, and it won't let you. (I'm sure there's a simple way around this, maybe by removing the cookies on your browser, but I kind of like the feature, so I haven't tried.)
Recommended for: Depressed people, people who aren't depressed but want to be, people who like very limited but meaningful choices, people who wished "I am Legend" had more walking and driving and less shooting at zombies.