I went and looked for a protocol spec as well. When I didn't see anything concrete on the site in the submission title, I poked around the comments a bit more and found a link to the Github issue[0] requesting detail with respect to the architecture of the TMTP protocol.
I further poked around in the appropriate places[1] but found nothing remotely related.
The protocol spec[2], while useful in defining the control mechanisms and message formats is vague or silent when it comes to a variety (too many to list completely here) of functional, operational and implementation issues.
A comparison of TMTP's spec with SMTP[3] ("the protocol at the root of all these problems"[2] with messaging), is quite illuminating.
While SMTP by itself lacks a variety of features, it provides a robust, interoperable architecture that's broadly supported and has been augmented repeatedly by other protocols (e.g., MIME, DMARC/DKIM, SMTP-AUTH, LDAP, etc.) to provide such features.
It's not clear to me that mnm/TMTP has been fleshed out enough to provide a real alternative to SMTP+extensions. Rather, it appears to be another (there are many) client/server messaging application that's not interoperable.
Should these issues be addressed, discussed and refined in the appropriate forums[4], It's possible that TMTP could turn out to be a viable replacement for SMTP.
I applaud the authors' work and hope they have much success with their entry in the messaging app market.
[0] https://github.com/networkimprov/mnm/issues/5
[2] https://mnmnotmail.org/rationale.html
[3] https://tools.ietf.org/rfc/rfc5321.txt
[4] https://www.ietf.org/how/wgs/
Edit: Fixed links.