In the AI field, is it worth it to publish a paper that gains the same results as another but with a different method?
As you say, applying well-studied tool X to well-studied problem Y and getting the expected result won't lead to a groundbreaking paper. But not every paper is revolutionary, and many such papers are published, particularly in AI. It is true that professors and other senior researchers try to avoid publishing such papers simply because they have limited time and need to invest it on higher-impact ideas. Only mid- and high-tier papers really count when calculating, for example, tenure decisions.

But you are not a professor, you are 14 and this is presumably your first long-term project. Writing something up and getting it "out there" is highly worthwhile, both so you can practice writing publications and so that you have something citeable when you apply to college and beyond. Even a low-tier publication, or putting it on the arXiv, is pretty darn impressive at your career stage.

I assume this is why your professor recommended that you write up something to publish. Either that, or he thinks the work is more significant than you realize. Since he is familiar with your work and we are not, I would defer to his advice in any case.