Zoro vs King doesn't really make sense. Zoro's coughing up blood and took hits from a Yonko. He needs to recover. Besides he has to meet up with Hiyori, help her kill Orochi and we need to get a flashback about his family. I think it's clear that his main fight is with Kaido.
Zoro was also in the dome with King for 10 chapters but they didn't interact once. Zoro's interacted more with Apoo and Queen then King.