Unfortunately, it's not possible to install just the new Library module into a legacy JohnCMS installation.
The current development version has been significantly refactored, so the new Library depends on changes made throughout the framework, not only inside the module itself. That's why simply copying files results in errors.
If you want to use the new Library implementation now, it will be much easier to install the current development version of JohnCMS from the repository instead of trying to adapt the new module to an older release.
Installation instructions are available here:
https://github.com/johncms/johncms#installation-from-repository
Otherwise, I'd recommend waiting for the next official release if you prefer to stay on a stable version.