Before we delve into the game, a little explanation about the maker is in order. In the late summer of 1986, the then-fledgling Square announced a joint venture with six other computer game companies to create new games exclusively for the Disk System. That venture was called - da da dum - "DOG", standing for "Disk Original Group". In the magazines of the time DOG introduced all sorts of wacky titles, including a side scrolling RPG named Excalibur, a 30s gang simulation called Chicago Connection, and an action RPG called - of all things - Dark Side of the Moon. None of these titles have been heard from again, but the silliest of the lot found release as Apple Town Story.
This game is more or less a port of the 1984 Activision computer title Little Computer People, which anyone around at the time remembers fondly if they had lots and lots of free time on their hands. The game wasn't really a game; load it up and you see the cross-section of a house. A little dude - the person that lives inside your computer and makes it work - enters the house and takes up residence. As Activision said, the guy was always in your computer; you just gave it someplace to live in. You could watch the guy go through daily life, send it stuff to do, give him a pat on the head - whatever you want. The idea is to have fun interacting with your little computer person and seeing what stuff it'll do - voyeurism for kids.
The main charm of the "game" is that there's no need to grip the controller the whole time. If you want you can put the controller away, grab a beer and just watch Lucy/Cathy and her cat bop all around the room. She'll get mad at you if you do nothing to entertain her, though. That's why you have eight commands at your disposal; you can send her some food or a Famicom game, ask her to play the piano, call her on the phone and so on. Whether she follows what you say or not is her choice, but the idea is that it's fun to see her reactions.
Although one can't forget the influence this game might have had on newer stuff like Tamagotchi and Princess Maker, there's no need to bore yourself to death keeping this game on all day.