Yes as Mom says, you need to inform the embassy of the birth. As your medicals have expired, you will need to repeat them, and most likely they will need a medical report for the baby. Don't repeat the medicals until the embassy tells you to do so, but you might want to check with the physician about fees and scheduling of the medicals. Make sure they won't need any document from the embassy to perform a medical for the baby. All of that checking just helps you be prepared. . They will need to request the correct number of visa slots if/when your case clears.
Now, the email response was unusually specific. When they mentioned the "Eligibility Review Unit" it would suggest they had to send your documents to a central processing unit (within KCC) OR, more likely the ERU is some function within each embassy. The marriage cert is probably what required that check - I assume you interviewed at an embassy which was not used to seeing marriage certs from countries where polygamy is practiced.