I hadn't heard the term library operating system before, but what is described at that link is nothing like your project.
The "kernel" referred to at that link is a full actual kernel, with networking, proceed scheduling, device drivers and hardware access, etc. It means the full implementation of those features. The reason it can be linked into the application's process as a library is because it's taking about a situation where there's only a single application running on the whole machine (presumably a virtual machine). The kernel and application then run together in a single memory space, with the kernel code (maybe the whole thing?) running in kernel mode.
You have implemented the user mode API that makes system calls to the (Windows) kernel. That is not a kernel in any sense. It is confusing and wrong to call it a kernel.
The "kernel" referred to at that link is a full actual kernel, with networking, proceed scheduling, device drivers and hardware access, etc. It means the full implementation of those features. The reason it can be linked into the application's process as a library is because it's taking about a situation where there's only a single application running on the whole machine (presumably a virtual machine). The kernel and application then run together in a single memory space, with the kernel code (maybe the whole thing?) running in kernel mode.
You have implemented the user mode API that makes system calls to the (Windows) kernel. That is not a kernel in any sense. It is confusing and wrong to call it a kernel.