Thanks! I write my code in C, and use the emscripten compiler. It has some functions to call out to native javascript. From there I just put a value in localStorage if the player has started the game once! Here's the documentation and the code in the game.
If you're more used to writing with an engine, I would search for something like "call javascript functions from unity in html5 builds"
And if you'd like to play more, you can always play the original 100 EYES, but be warned it's harder!