In order to read events and modify devices, libinput needs a file descriptor to the /dev/input/event node. But those files are only accessible by the root user. If libinput were to open these directly, we would force any process that uses libinput to have sufficient privileges to open those files. But these days everyone tries to reduce a processes privileges wherever possible, so libinput simply delegates opening and closing the file descriptors to the caller.
The functions to create a libinput context take a parameter of type struct libinput_interface. This is an non-opaque struct with two function pointers: "open_restricted" and "close_restricted". Whenever libinput needs to open or close a file, it calls the respective function. For open_restricted() libinput expects the caller to return an fd with the given flags.
In the simplest case, a caller can merely call open() and close(). This is what the debugging tools do (and the test suite). But obviously this means you have to run those as root. The main wayland compositors (weston, mutter, kwin, ...) instead forward the request to systemd-logind. That then opens the event node and returns the fd which is passed to libinput. And voila, the compositors don't need to run as root, libinput doesn't have to know how the fd is opened and everybody wins. Plus, logind will mute the fd on VT-switch, so we can't leak keyboard events.
In the X.org case it's a combination of the two. When the server runs with systemd-logind enabled, it will open the fd before the driver initialises the device. During the init stage, libinput asks the xf86-input-libinput driver to open the device node. The driver forwards the request to the server which simply returns the already-open fd. When the server runs without systemd-logind, the server opens the file normally with a standard open() call.
So in summary: you can easily run libinput without systemd-logind but you'll have to figure out how to get the required privileges to open device nodes. For anything more than a test or debugging program, I recommend using systemd-logind.