Responding to papers which reinvent ideas without citing them
From what you have described, it is unlikely that the author's decision to omit mention of the previous paper would constitute any breach of the journal's policies, or any violation of academic integrity requirements.  You have stated your assessment that this is not a case of plagiarism, notwithstanding some similarities between the present paper and the previous paper.  If that assessment is correct then you are really just talking about a decision by the author to omit mention of a previous paper, which is a decision that is within his discretion as a researcher, and which has gone successfully through peer review.

Since there is no evident breach of policies or academic integrity standards, the journal is unlikely to change the article unless its authors request an addendum.  You could either write to the authors suggesting this, or you could try to publish your own "letter to the editor" supplementing the information in the recently published paper by mentioning the previous work.  A letter to the editor could draw attention to the omitted work in a respectful way, noting the similarities of the ideas in the two papers, and noting the way in which the present paper formalises the previous idea with a new model.  That would make a nice supplement for readers who are unfamiliar with the previous work.  Of course, there is no guarantee that the editors would publish it, but if you feel strongly about this, it might be worth a try.  If you can say something valuable about the connection between the two papers then the editors might decide that it is a worthy supplement.