I think this article title is a bit misleading. When I think "old-school watch makers" I think of something like Rolex or Breitling, the high end painstakingly crafted watches that are as much about art, engineering, style, and "look at how much money I can spend" as they are about telling time. I don't think the Apple Watch poses much of a threat to these companies, at least not in the near future.
The body of the article is more clear, showing that midrange watch makers are likely to suffer, which I think is a reasonable prediction to make.