In RPG-style games, which this is... sort of..., "end game" generally refers to the point where you've built up your character to the maximum, or very close to it, and are now concerned with other things. It used to be known as the "elder game" in MMORPGs.
I somehow interpreted as if the character in the dark room had dreamed everything, and just woke up. And then the cycle start again. Seems fitting for the game.
Comment from the source file in the endGame function :
// Restart everything! Play FOREVER!
However, "End game" usually refers to the gameplay at the end of the game, specifically in chess where you try to force mate with only a few pieces.