Well they need to pay someone to clean up the dog park, and pay for the dog park itself. I know I have seen people in our travels use the dog park and not clean up after their animals. There is always that one person.
They also figure you will be using additional water, animals need to drink ?
And at 5 bucks it is one of the best deals at Disney.
We have two dogs and they always only charge us $5 per day. I questioned it and was told it's not a per pet charge. Maybe it depends on who checks you in.