The importance of "Play"

I sit on my back porch and watch the squirrels that live in or around my yard, scurry along the top of the fence, jump from tree branch to tree branch, run through the yard and drop acorns on my driveway. All the while, my German Shepherd is chasing them. She doesn't bark or growl. Her hair stays laid down. She gives off all the cues that she is simply at play.

I have no psychology or zoology background and I've always believed that there was an order of intelligence levels directly related to an animals brain size. I believe dogs want to play because they are intelligent.

This led to my considerations of the squirrels' intelligence. Are the squirrels ignoring my dog and just carrying out their daily duties being careful to avoid the danger of this large beast in their feeding area or do they have the mental capacity to share in her same want to play? Is there an instinctive need to play?

Of course, I went to the internet and googled "Are squirrels intentionally fricking with my dog?"

What I came across (besides all the ads for dog toys and images of squirrels), was a TEDtalks video of Stuart Brown's presentation on the importance of play. This 30 minute video addresses a lot more than just my original question and offers a correlation between mental health, productivity and emotional stability when play is either introduced or withheld.