What do you mean by "Unix"? Are you talking about some specific Unix version, or is there something in the POSIX spec that says that libc isn't a library?

It's not that libc is supposed to not be a library, but those functions are the POSIX-defined interfaces to the OS. Linux is unusual in that it defines its stable interfaces in terms of the syscall ABI, enabling different implementations of the libc that can work semi-reliably across kernel versions.