There's a whole genre of games like this these days. I really think of A Dark Room and Candy Box as some of the best and more recent ones don't seem to really put much effort into it, though they can still be pretty engaging. The search term for them is "idle games" and I'd have sent you the way of the subreddit for them which has a comprehensive list, but they all seem to be set to private.

This one looks to be up: https://www.reddit.com/r/incremental_games

Thanks for mentioning that this isn't the ONLY one of these. I probably could have guessed eventually, but now I'm absolutely fascinated. Such a cool opportunity to build simple games with the potential for infinite expansion.

http://www.kongregate.com/idle-games, a bunch of the idle games submitted to Kongregate. Not sure when it all started but in like last year kong recognized it as its own genre. However the kitten game seems to be a bit more complex than a lot of the ones kongregate is hosting.