Do I understand correctly that nolibc is just another implementation of the C standard library in terms of Linux syscalls? Comparably to, say, musl libc?
No it's not comparable to musl libc. Standard I/O functions don't support buffering and the printf implementation can't print floats, for example.
glibc is a space shuttle, musl is a hatchback, nolibc is a skateboard
They all do the same thing (take you from A to B), but offer different levels of comfort, efficiency and utility :)