Please explain how this DIFFERS from any other valid "cease & desist" copyright letter. Answer: they don't. That was my point.
Well, no. (And by "no", I don't mean they don't differ; I mean that you're still wrong.) Have you ever heard the standard advice about what to do when you find yourself in a hole?
A DMCA takedown notice - which this wasn't, and which you apparently blathered about the abuse of in several of your posts - is a special and particular type of cease and desist. A notice containing the required elements carries with it certain specific legal rights and imposes specific obligations and timelines on the parties.
Among (several) other things, it triggers a specific, detailed process by which a party accused of infringement can send a counternotice to its ISP, asserting that the material is non-infringing. Such a counternotice (following the DMCA-prescribed format, with what you might refer to as the appropriate "magic wording") has the very useful property of protecting the ISP from liability for contributory infringement if they restore online access to the material in question (after a specified waiting period elapses). It also imposes a specific, short timeline on the original complainant to file suit if they dispute the counternotice: a "put up or shut up" requirement. You can find this stuff in section 512(g) of the law I linked earlier.
To summarize--not all actions relating to copyrighted material online will necessarily involve law made or amended by the DMCA, and not all takedown requests are DMCA notices. Finally, I'm done trying to educate you.