(I have only briefly skimmed the article, but ...)
Material such as this serves to remind the reader of what they already know, and contextualize it in a way that is relevant to this article. The article begins by telling the reader, "We all know what scalars and vectors are---here they are---but have you wondered what if ...", and taking the reader beyond. The introduction which you seem to find objectionable is only a small part of a much longer article.
In addition, different readers have different, mildly different notation styles. These introductory blobs inform the reader of the language in the article, and are essentially a friendly statement of definitions.
A third purpose is rhetorical: readers sometimes get stuck while reading text, and these parts of the article work as anchor points where they can loop back and "synchronize" with the writer.
Material such as this serves to remind the reader of what they already know, and contextualize it in a way that is relevant to this article. The article begins by telling the reader, "We all know what scalars and vectors are---here they are---but have you wondered what if ...", and taking the reader beyond. The introduction which you seem to find objectionable is only a small part of a much longer article.
In addition, different readers have different, mildly different notation styles. These introductory blobs inform the reader of the language in the article, and are essentially a friendly statement of definitions.
A third purpose is rhetorical: readers sometimes get stuck while reading text, and these parts of the article work as anchor points where they can loop back and "synchronize" with the writer.