Incomplete and Complete mean that the mangaka is still working on it or has finished it, it has nothing to do with what's posted here. It says that at the top of this page...
"You've finished reading all chapters we have available for Koigokoro wa Neko o mo Nurasu which is currently marked as completed, this is the status of the releases by author, scanlations could still be released!"
Uh... This is an illegal website therefore original authors are not posting their works here. I was referring to the tag and icon. before it's an open book tag and now it's in a closed blue book tag - meaning the user who posted this probably confirmed with mangago that this is completed now. Regarding the chapters, it may or may not be updated. Depending of who wishes to post/upload the chapter.
The uploader only included the stories of the main couple. There are other chapters but they're different stories. You can look on r*nta and see the table of contents.
Why did it become complete after 3 years? Last time I read this it was still incomplete w/ 3 chapters. Now I felt suspicious and thought this was dropped. It so felt incomplete for me