Board Thread:Questions and Answers/@comment-32397673-20170626124121/@comment-25144197-20171230222320

In the credits for the movie, you can see shots of them meeting Asuna's mother, the ring Kirito gave her and them snuggling on a  train. And youtube ocommentator Airspeedprime says he believe's it i is "their actual engagement ring". Also take into account delevopment at the end of the SAO II second arc with her mother. You do the math.