I spent about an hour in the game and found a few cool things/secrets. I don't know if the game has a proper ending other than the taking a nap thing, but here is what I found: (spoilers ahead)
There is a white gate in the first room. I don't know if it can be opened.
The white dog in the next part of the park has a bone. If you dig a hole, you can put the bone in the hole, and the dog will wag her tail.
There are two parts of the map that have an X on them instead of the normal dots. Digging here reveals two colored pixels. It might be some sort of nut? It's hard to tell. If you fill the hole in again, the nut stays on top. There are two places where there are X. I tried pushing the squirrel onto the nut. Nothing happened.
Behind one of the grass patches, there is some sort of meat. Probably chicken. When you eat it, you get a bone. This bone can be given to the big dog, which allows you to go through and get the game's ending. When you finish the meat on the bone, a black squiggle spawns. I don't know what it is supposed to be. You can push it around.
There is a duck who can follow you around. He will follow you anywhere until you change direction. Then you have to get him to follow you again. I found a way to use him with the two balls in the park. The balls normally keep going until they hit a wall. But they also stop when they hit the duck. By strategically moving the duck, I can get the balls to any place on the map. I'm not sure if I can do anything with this though.