Why is that woman considerd the woman that Rimuru is destined to be with? In episode 6, we learn that


  Shizu


is the woman Rimuru is destined to be with.  She shows up in the next episode.


  She also dies a couple of episodes later, the next day in-universe.  Aside from her showing up in the OP and ED, and being a quest-giver (for Rimuru to be a teacher) several episodes later, she doesn't have much going on in the series.


Why is she considered so important and "Rimuru's destiny"?  Why is she seemingly more important than Veldora, the ogre women, Miliam, etc?


   Why is she more important than any of the other monsters/spirits that Rimuru absorbed?


I'm only familiar with the anime, so if the manga/LN goes that much more in detail about this, then don't spoil it and leave the answer somewhat vague.
@earthling gave a good answer into the importance of her role in Rimaru's destiny. Below I want to give the ways in which she was always with him. 


Shizu was with Rimaru physically, forever, in his stomach.
Shizu also lived on with him when Rimaru took her physical form.
In a sense, she was also with him through the emotional connection of fulfilling her wishes. It's often said that a person lives on through their legacy and the memory of others. Rimaru fulfilled her wish and legacy of saving the Children. Shizu also lived on with him both in his memory and in Rimaru's journey to finish her quest of confronting Demon Lord Leon Cromwell. 


So in many ways, she was always with him and thus was the person he was destined to and ended up being with.