The simplest way I can think of is to just install a stock distro, activate automatic login for an account that doesn't have any admin privileges, then have your game added to autostart.

Since you're creating the game, I would add an option to launch it in 'kiosk' mode, where any menu option to 'quit' is removed.

You can get more fancy of course, but I'm assuming you want to focus on developing your game rather than configuring Linux ; )