The short answer is: why not?
According to Wikipedia:
Creativity is a phenomenon whereby something new and valuable is formed
I'll describe a few ideas in this article, but they aren't new. So, is this article a creative work?
According to the definition - yes, it requires some combination of my current knowledge, thus creating a new way to deliver such a topic. It's valuable because someone will find new ideas here. However, the very ideas aren't new, and one may find a different way of delivering them on the Internet.
Can a natural language generation model create such an article? Not quite like this, but a similar one that will be better and worse, depending on the random selection of many generated texts. So, yes, it can already.
Can we presume the same for music, movies, and image creation? With a working model and many examples, this is what neural networks do today. The quality of that art is disputable and depends on the patterns and story complexity.
What is new?
The "new" in the creativity definition is significantly relative. This article is original only in terms of deliverability to readers. The hand-drawn images here are authentic only in my unique hand movements, not in the ideas they present. Therefore, re-creating a similar article by the models trained on a lot of data is possible.
Let's assume the originality of my ideas in this article is 0.0001 out of 1. And let's assume that Einstein's theory of relativity is 1. The models that generate text may reach a similar to this article, relatively small originality score because they combine the examples given to them by humans. They can't produce a 0.9 of 1 of the novelty score if they work like pattern distinguishing algorithms.
Humans are pattern distinguishers too. However, some of us can produce more novelty in our ideas. But we're entirely different than those programs, aren't we? Yes, we are because we aren't merely pattern recognizers. Instead, we can understand the information and create models of how the world works. The neural network models don't do that.
A program that creates models
How can humans do that? We have a model for this, but we don't know how it works in reality. Our brain is astonishingly complex. The cells there, as in any other tissues in our body, are created by other cells' that have instructions on how to do so. The living organisms' cells know how to encode the instructions and then extract them to make new cells.
The instructions don't necessarily tell every brain cell how to think about something; they're telling cells how to function. And then you have billions of such cells that work together, forming a complex structure. So DNA instructions don't convey to a brain cell how to think, but they contain a base set of instructions to let it function with other such cells and transmit signals.
We're programmed. But our "codebase" is much more complicated than any other one. We're programmed to create models, understand, and recognize patterns. Thus, we can produce more novelty in the existing ideas.
Can we program machines to do so? It's possible in principle because it's possible with humans. But, can we, humans, program a machine to think? It requires us to create a model of how we work(we still don't know many things about how we function). Or to create a model of how a machine may construct models. I.e., a hypothesis, not an exact human "program" reproduction.
It's possible to program creativity in machines, in principle. We were programmed(not necessarily by something, it might be a random coincidence), so why it's not possible with other matter? The different question is if humans can do that. And the answer depends on our mental ability to understand how to create a working model that can "think." In a digital world, it's called AI. But who knows, maybe we'll be programming stones.