Whether newspaper articles count as a publication depends on the context.
In the general academic context, newspaper articles don't count as an academic publication.
Generally, the main works that count as academic publications are:
- peer reviewed academic journal articles
- academic books and book chapters, and
- full-text peer reviewed academic conference articles.
Academic context - newspaper articles are not academic publications: So in general, if you are asked how many publications you have in an academic context, it will generally just be the above that gets counted. In other cases, you might only be being asked about a count of peer reviewed journal articles.
This kind of context often applies to job applications, grant applications, promotions and so on.
Showing how newspaper articles contribute to track-record: That said, in most academic contexts where your track-record is being judged, there is scope to communicate external engagement. Publishing in newspapers is one of many possible examples of external engagement. And in some cases there may be merit in listing the specific instances of external engagement (e.g., particular newspaper articles and so on).
Furthermore, the value assigned to writing newspaper articles varies substantially between fields, universities, and departments. For example, I briefly worked in a business school and they placed a lot of value on academics engaging with the media, and particularly the popular business press. I imagine this was related to the branding benefits associated with their academics being read by the business people who complete their courses. In contrast, in more pure-science disciplines, engagement with the media was really an optional extra.