If it is not a temporary endeavor, I think the term "project" does not fit well.
But you did not only ask if the term "project" applies, but also "can these project management methods and frameworks be applied?". Sure, you can probably try to use a full-blown project management approach for iterative software development by interpreting each cycle as a mini-project. However, this is IMHO somewhat the wrong question, because it gives you a misleading answer.
The real question you should ask is: does this make any sense? Or are you just shoehorning a situation into some kind of management method which does not really fit?
What you describe is what I would call "product development", as opposed to "project development". To my experience, product development, especially when done with a small team and in cycles of length of 3 weeks at maximum, simply does not require lots of the heavyweight stuff from the project management methods you mentioned. Especially anything like "several hundred pages requirements specs", "a monthly status reports of a dozen pages" or "tracking progress using large GANTT diagrams" are mostly obsolete if a product is evolved in small cycles.
That does not mean there is never a need for "project management" in product development. Especially when you start with a new product, or when you plan a new "major release" or a new module for the product with a given specification, defined goals and a fixed time frame, then this can require classical project management methods. However, at least when such a new version or module is "finished", and maintenance as well as short-cycle evolvement starts, these methods are seldom helpful, and agile methods like Scrum will be much better suited.