I'm not sure, but from what I understood, It seems that those scenes were altered versions of the real memories. It's a bit confusing, though. Maybe she was originally with someone else (her opponent?) but was replaced by Klein, like in the last memory with Asuna and Yui, where Klein took Kirito's place.
It was an interesting chapter, though. I know it was just posted, but I already can't wait for the next one, hahaha