Welcome, @john_zhang. I think the core of your question is what does prediction have to do with intelligence. Before I go into that specifically, let me address a couple of your other points.
First, you appear to have the impression that folks who are working on HTM theory believe pure prediction by itself will magically lead to intelligence. I don’t think anyone here who understands HTM would make that argument. Prediction is part of intelligence – an important part of it. But there are other parts which are just as important, like movement and agency. HTM theory is some time away from describing intelligence.
Second, you give the example of RNN, and ask what makes HTM better. The current implementations of HTM won’t beat RNN at very many tasks (one big reason for this is because HTM does not yet incorporate hierarchy, despite its name). At some tasks, on the other hand, HTM is better. For example, HTM’s ability for one-shot learning means that it requires orders of magnitude less training to learn sequences compared to RNN. It also has an advantage in its resistance to error, noise, and the catastrophic forgetting problem.
So getting back to your central question (if I understand it correctly), what does prediction have to do with intelligence? I believe the answer to that is to think of why intelligence exists in the first place. Intelligence exists in order to increase the survival rate of of an organism. The reason organisms are able to survive and make copies of themselves into the future, is because they are capable of resisting entropy. Any orderly system which is not able to resist entropy will disintegrate and become random chaos. This is a basic law of the universe.
Ok, so what does that have to do with anything? Well, in order to resist this tendency toward chaos, an organism must be able to model the world around it. This allows it to make predictions about what will occur. Like I mentioned before, that alone isn’t enough, though – simply knowing what will happen alone won’t enable an organism to resist entropy. What is also needed, in addition to prediction, is the agency to act on those predictions.
If you’ve not read about the Free Energy Principle, I highly recommend it. I think it cuts to the core of your question, if I understand what you are asking. This video does a pretty good job of explaining the basic concept.
One additional point which you did not mention, but which I believe is important, is why one would explore the biology of intelligence, and what advantage that approach may have over the more traditional approaches. For that question, I think Matt did a great job of explaining in this video.