I think it's quite simple.
rmdir TESTD succeeds, then the two links which refer to it,
TESTD are removed. So the link count of the specified directory is reduced by 2. This can be verified by running a shell inside the directory and running
ls -ld after the directory has been unlinked (removed from its parent).
Once a file (such as a directory) has 0 links, and no running processes with a reference (file descriptor or current directory), it will be truly deleted.
You can try to observe true deletion by looking at the used disk blocks in
df .. It works in Linux
ext4 filesystems. Other filesystems may have more complex optimizations though, making it harder to observe.
rmdir fails if "pathname contains entries other than . and .. ; or, pathname has .. as its final component." (
man 2 rmdir). After
rmdir succeeds, the directory will be completely empty. This guarantees that there are no sub-directories, so they won't have any
.. links, to keep the directory's link count above 0.