Looking at the source code[1], it appears to be analogous to MinGW in the MinGW:GNU/Linux:Windows relationship, but replace with MinC:BSD:Windows. In other words, a minimal user-mode layer that presents BSD headers (and therefore BSD symbols, macros, and types), libraries, and core utils to end-users, thus abstracting over MSVC†.
EDIT: replace 'MinGW' with 'Cygwin' above. So it is Cygwin.
I'd say calling it a 'kernel' is quite a stretch—there is not much that runs in kernel-mode, and everything runs atop the NT kernel which does the actual 'kernel'y stuff.
[1]: https://github.com/dboland/minc
†: Until one wants to use very recent and very nice Microsoft libraries[2][3], and these fail spectacularly because MinGW doesn't know about nice MSVC-specific stuff like SAL annotations[4].
[2]: https://github.com/microsoft/wil
[3]: https://github.com/Azure/azure-sdk-for-cpp
[4]: https://learn.microsoft.com/en-gb/cpp/c-runtime-library/sal-...