Here i utilized the paw shape in green to form an abstract of a pet face, where i highlighted on the eyes by adding two white pupils to show the eye better and the other outer side of the paws look like as if they formed the ear and to highlight the nose, i added a heart shape and on the outside is a big smile in blue.
So the by looking at it, you will notice right away, a smile, a pet face and a paw :)
I think this is incredibly clever. I'm a little afraid that it takes too long to discern what is going on (it took a minute to see the dog face).
Looking at your idea gave me a thought. I wonder if you could use the word "dog" itself to become an abstract drawing of a dog (I wish I could draw). The downward loop on the lower case "g" becomes the nose, the circle of the "g" can be used as the face, and the upward line on the "d" can become the tail. Just a thought.
I'm glad you noticed how incredibly clever this is. I like to create unique and clever marks that deliver a good message behind it, this way it stays longer and can be used effectively in different mediums.
As for your idea that evolved of mine now, will give it a try and show it to you.