Why does my dog have a dry hacking cough?

A cough could be a number of things, almost all of which need to get evaluated by a vet. If your dog coughs once and that's that (maybe after playing rough or eating/drinking quickly), I wouldn't necessarily worry about it. However, coughing could mean that there's something else going on, like heart disease, heartworm, pneumonia, collapsing trachea, fungal infections, kennel cough, allergies, cancer, etc. If there are other symptoms that your dog is showing, like lethargy, labored breathing, runny nose, pale gums, etc., then you definitely need to be taking your dog in for an exam as soon as possible.

Sounds like your dog may have Kennel Cough, which is contagious to other dogs. I would recommend taking him to the vet so they can get him on medications.