How to refer to a methodology that consists of jumping from reference to reference?
The "method" you describe is probably not rigorous enough to be called a method in the scientific sense. There is a lack of rigor apparent in your admission that you swung "from reference to reference until I had a good argument." The quote suggests some bias in the procedure and in your selection of information, and your search strategy doesn't seem to be reproducible.

There is a method called "systematic review" that ist different from what you describe by its (relative) objectivity and reproducibility.

But more than a method, what you applied is a common practice that most researchers apply, without thinking much about it, to find literature to include in a review section or in a review-type article. If swinging from "reference to reference" involves going through the references of each paper you dug up, and looking at their references etc., you could call it "a snowball procedure".

However, fancy words won't impress a reviewer. As far as the review is concerned, I would not suggest to claim that you applied a rigorous method if you didn't. Rather, I would reframe the purpose of your paper: Call it a state of the art review, or an exploration of some topic.