I think that's pretty pedantic. When most people here say 'Linux Desktop', they mean the Linux kernel, GNU(-ish) userland, Wayland/X11, and some desktop like GNOME, KDE or Mate.

Though, I guess outside tech circles, people will just talk about Linux as the whole desktop OS. E.g. our municipality was promoting installing a Linux distribution to save Windows laptops after the Windows 10 apocalypse, and they just call it Linux.

Even Wikipedia says: Linux (/ˈlɪnʊks/ LIN-uuks[15]) is a family of open source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds.