Hello Terence Chase,
Welcome to the Microsoft Q&A Platform. Thank you for reaching out & I hope you are doing well.
NOTE: As an original poster cannot accept their own answer, I am reposting it so that you can accept it an answer. Accepted answer will help other community members navigate to the appropriate solutions.
Issue: How do I add a second domain name to my primary domain using the Azure DNS?
Solution: there is no way to point the new domain extension to the primary domain without an IP address. Using an A record directs the new traffic to the web site, which I guess was the point.
If the above response helps answer your question, remember to "Accept Answer" and "Upvote it" so that others in the community facing similar issues can easily find the solution. Your contribution is highly appreciated.
Looking forward to your response and appreciate your time on this.
With regards,
Ganesh