I don't believe that it was an outright threat. I think that Michael mentioned who he was to Vitelli because it was obvious that he could no longer hide who he was once the encounter was made. I think that his speech to Vitelli was more to let him know that retribution would be swift and sure if he betrayed the Corleones. As said here, Vitelli also saw a better life for his daughter and all of his family if she could marry into such a family, and live in America. I wonder if Michael ever took care of her family after she died?