IATA is a commercial organisation which have nothing to do with operations and flight safety even they presenting themselves in this way too. So there are 2-letter IATA designators assigned to non-airlines, and I recall there are some designators assigned to non-aviation companies.
The sub-discussion was about with whom passengers are actually doing business when booking a flight with Manx2, i.e. about contractual issues, not about oversight and licensing.
Anyway, I think it is a safe bet that Manx2 does not use the IATA code "NM" of its main partner airline without the knowledge and authorization of that airline. And if you check the IATA database, no IATA code has been issued to Manx2 - although you are correct that they also issue codes to non-airlines (e.g. railway companies).
Btw, as far as ICAO codes are concerned, there is similar confusion. Manx2 is often mentioned in connection with the ICAO Code "BPS", which happens to be the ICAO code of Budapest Air Services, the company that initially operated the Let 410s for Manx2 before Manx2 switchted to Slovak carrier VanAir.