What is Windows 8 core?

The "Core" from "Windows 8 Core" simply emphasizes it is the "plain" Windows 8 and not one of the other versions (Pro, Enterprise, RT).

Paul Thurrott of WinSuperSite explicitly names Windows 8 Core in his giant comparison table of different Windows 8 editions (notice the plain "Windows 8" is absent from the table because it is referred to as "Core"):

More information about the different editions of Windows 8.

Windows 8 (Core) is simply Windows 8. It's the base (core) product, which Pro and Enterprise built on.

And I say that because I can find no official reference to a Core product and it was in parenthesis in your source (compared to the other editions where no parenthesis was used).