“Bordetella bronchiseptica is a small, Gram-negative, rod-shaped bacterium of the genus Bordetella.” - Wikipedia

“Kennel cough” is a set of symptoms, not a specific disease. Bordetella is merely the most common cause of this symptom set, and has a vaccine available. This is the reason that dogs vaccinated against Bordetella can still get kennel cough.

The primary reason for antibiotics with a bad case of Kennel Cough is to prevent bacterial pneumonia.