The most heartwarming about this story is the total lack of angst. They never had any doubts about each other's love and commitnent. Even the family was "oh well, that was obvious".
It can only work for a short story though.
You could have the exact same story elements in a long series, though. There would need to be added conflict of course, but that could easily arise out of their careers, personal conflicts with others, maybe friends or Emi's cow-orkers who don't accept them, etc. without having to make their relationship or devotion to each other any different.
What we have here would be a framework in a longer piece, tonnes of space to fit in all the little, and sometimes big, things a person, or a couple, faces in their lives.