I'll try and make it very simple.
Zoro's opponent ever since he got Enma was Kaido, no one else.
He makes it clear at the very beginning of the raid that his goal is Kaido.
Again, 9 chapters later, Zoro reaffirms that he wants to go to Kaido.
Notice what Luffy says? He demands everyone to handle everything besides the defeat of Kaido. However, 8 chapters later, what do we get? We get Zoro declaring that he's only come to Onigashima to kill Kaido. Does this suggest that in Zoro's mind, there's a difference between killing Kaido (what he plans on doing) and beating Kaido (what Luffy plans on doing)? This is the only way I can make sense of this without having Zoro completely disrespecting and disregarding his captain's wishes.
While on the rooftop, we see Zoro attempting mainly finishing moves on Kaido except for his Black Rope Dragon Twister. Though, with the Dragon Twister, Zoro had a different idea in mind. Instead of killing Kaido, he wanted to save Luffy from being eaten. As far as I'm aware, Oni Giri, Hiryu Kaen, and Asura are all finishing moves with the idea being to kill Kaido. Unfortunately for Zoro and Luffy, both fail at their goals. Luffy doesn't manage to defeat Kaido and Zoro doesn't manage to kill him.
The interesting here to note is that Zoro's parallel with Oden has come full circle.
Oden meets a 26-year-old woman named Toki and is nursed by her.
Zoro meets a 26-year-old woman named Hiyori and is nursed by her.
An enraged Oden attempts to kill Orochi, fails, then shifts his focus to Kaido.
An enraged Zoro attempts to kill Orochi, fails, then shifts his focus to Kaido.
Oden fails in killing Kaido and only manages to scar him.
Zoro fails in killing Kaido and only manages to scar him.
This is why Asura is meant to be a disappointing moment for Zoro. He quite literally failed to achieve what he wanted to do and goes down while wishing he did more. Unfortunately, fans who dislike the idea of Zoro doing anything more to Kaido have turned it into a hype and fun moment. "Finally, Zoro got his moment, now get out of the way" type mentality...
Zoro has now completed the parallel between him and the unsuccessful samurai Oden. However, unlike Oden, he will have the chance to mirror what the successful samurai Ryuma did afterwards.
Lastly, unless you think Zoro fighting Kaido was just a random choice by Oda. Then Zoro fighting anyone besides Kaido will be a delay similar to Apoo.
King, Queen, or whoever it is, it doesn't matter. They're only delays to Zoro's actual goal.
Both Luffy and Zoro went down before achieving what they wanted to do, it's clear that by the end of the arc, they will both achieve their respective goals.
