Publishing a comment or contacting the authors privately?
There is nothing stopping you from contacting the authors directly. In fact that might be polite. It may, however, be unfruitful. Submitting a comment is not considered less polite than contacting the authors directly first. Remember, the authors have, in your view, published poorly referenced/researched work (reviewers and editors are partly also to be blamed). By writing a letter/comment, you perform a scientific debate where you wish to correct a problem with said paper and that is clearly within the realm of what we can and should do as scientists without feeling impolite.

Before you do anything you should perhaps solicit colleagues to discuss the matter over. Since the results have been published, some form of publication discussing the problem must also appear in a publication. It is for this reason you should carefully discuss the matter, start writing a "letter to the editor" of the journal where it was published. The letter should contain the information that puts the "novelty" in perspective. Under such circumstances the authors will have the possibility of a rebuttal which typically is published at the same time as your letter, it is their opportunity to "defend" themselves. This is what typically is done.

Now several things might happen, for example, the authors get angry, the editor refuses to publish your letter. This is why you are better off not being alone behind anything you write. If the letter is refused, then publish it elsewhere. But, remember, the point of writing a letter is to set the faulty perspective of the paper in a more correct one so that the paper is not taking credit where not credit should be had. Do not stray from this endeavour.