(going along with the idea that Cecil is a normal radio host who’s just bored and making up stories found here)  

Imagine that there’s actually nothing wrong with the dog park.  It’s just that Cecil is a dog person, and the dogs of Night Vale are full of loyal, physically adorable breeds that put a smile on Cecil’s face.  Except he can’t afford a pup, because the breeds of Night Vale are beautifully expensive.  So he avoids the dog park because seeing the dogs makes him sad that he can’t have one.  The hooded figures are the wealthy citizens of Night Vale who can afford the luxury dogs.  Who walk around with them, flaunting the fact that they can afford them.  They probably don’t even play with them, they just show them off, and it irritates Cecil to no end.