Based on the way that the word “encyclical” has been used in history, I am of the impression that all encyclicals are papal encyclicals. Some of these encyclicals were addressed to special audiences, and not always to the whole church. But, to answer your question, I think that the letters of St. Peter may be considered as encyclical letters (since St. Peter was our first Pope), but not those of the other NT writers, such as St. Paul or St. John. Of course, the letters of St. Peter were not called “encyclicals” back then, since the word was not used until the seventeenth century. Just my opinion.
You are right, of course, in saying that the letters of St. Peter are inspired, whereas those of other Popes are not inspired. However, I am not sure that to be “non-inspired” is part of the definition of an encyclical letter. Don’t you think that the fact of St. Peter’s letters being inspired gives it even more reason to be considered encyclical rather than not? After all, an encyclical letter, unlike ordinary letters, is one that is being circulated around its specific audience, rather than being addressed to, and kept by, just one person. And that is what St. Peter’s letters were. They were passed around from person to person, community to community, which comprised his audience. But, if what you mean to say is that the letters of St. Peter cannot be put in the same footing (on account of their being inspired) as the encyclical letters written by other Popes, then you are absolutely right.
They form part of Sacred Apostolic Tradition within Scriptures… Revealed Revelation.