This concept for a business is very cool, and it was not even a "yiddishe kup" that came up with it...

A company made up of, and owned by, non-Jewish IT specialists to provide IT support to hi-tech, and other, firms that do not operate on Shabbos.

Jewish-owned companies that are closed on Shabbos, especially if they are owned and managed by religious Jews, will generally not know about problems that might have cropped up in their company on Shabbos, and they definitely would not be able to fix them. They would not find out about it, or be able to fix it, until after Shabbos. Hiring a non-Jew to be on staff for Shabbos is also a problem if the owner of the company is religious.

A Druze computer guy came up with the idea after having worked at Microsoft. At the time a religious manager would sometimes ask him for help with checking for and  dealing with problems on Shabbos. After leaving Microsoft this Druze fellow decided to open his own "Shabbos Goy" company to provide Shabbos support to other companies that would not do it on their own but really need someone monitoring their systems and fixing problems on the day off.
(source: Bechadrei)

Even without being Jewish, he clearly has some sort of Yiddishe Kup. Maybe we should call it a Druish Kup