I'm pretty sure the dog is the only one there who understands the situation as play. The chicken is annoyed, and it's going for the eyes. If that was my dog I'd want to call it off before I ended up with a hefty vet's bill and a half-blind dog.
So far as I'm aware chickens (and ducks) have no instinct for play. A newly hatched chicken can fend for itself from the day it hatches; everything is instinct, they have almost nothing to learn so there's no need for play.
I do sort of agree with the sentiment though. When people tell me they wouldn't eat a dog because they're too intelligent, I tell them they've obviously never met a pig.