Animal Jam is kinda similar. You can adopt pets of all shape and color, and you can be an animal, too! It isn't web-paged based like this one, but instead you can immerse yourself in the world and virtually walk around. I really like the game.
You can join, and use my code!
https://buddy.animaljam.com/53YQBB5XTransformice isn't really like Chicken smoothe, but I'll tell you about it. It's a platformer game, where you are a mouse trying to get the cheese. Link is in the desc.