It is correct in terms of how people have used and still use the word that the Holocaust refers specifically to the 6 million Jews who were murdered and not to the other victims of genocide and the war. There strangely isn't an all-encompassing term for all the genocide that the Nazis did afaik, though you can refer to some of the different subsections of it with various names like Aktion T4 (the "euthanasia" campaigns against the disabled and mentally ill), and Generalplan Ost sometimes gets used as a shorthand for the genocide on the eastern front.

Edit: I do agree that the phrasing of this message at least suggests reinforcing an idea of Holocaust exceptionalism, the idea that the Holocaust was a unique evil that it's improper to compare other genocides to, which is obviously an extremely backwards and chauvinist attitude that is harmful to the whole of human civilization.