One possible reason why your dog may be walking like he is drunk is that he could have a vestibular disease. Vestibular disease is a condition that affects the inner ear and balance center of the brain and can cause a dog to become uncoordinated and unsteady on its feet.
If your dog displays other symptoms, such as head tilt, nystagmus (abnormal eye movements), and vomiting, then the vestibular disease is likely a culprit.
However, there are other possible causes of these symptoms, so it is best to have your dog examined by a veterinarian to rule out any other potential problems.