Kid : What is this ?
Kaido : Tatsumaki!!
Killer and Kidd : Wouahh!
Luffy : Thanks Zoro!
Zoro : That's actually not a simple tornado!
Zoro : oh shit!
Zoro : Luffy!!
Kaido : Gyaaa!! (Kaido wanted to try a new type of chewing gum)
Zoro : Wait! Wait ! Don't eat ...
Zoro : My captain!!
Zoro : Santoryu!
Kaido : hm ??
Kaido : This form of haki!!
Zoro : Kujou Ô Tatsumaki!!
Kaido : Uoooo!
Killer : (sorry the picture is cut but probably thinking what he gonna eat at KFC tonight)
Big Mom : That kid .. He managed to cut Kaido
Kaido : Oh .. i see it's working! That's Oden katana ?
Kaido : To think you challenged me with Tatsumaki, Uerororo"
We talk with @ivaannom so before claiming lots of things, we agree that 正体 means form or identity.
So Kaido is seeing here that Zoro is using the same haki of Oden "Ryou", exactly like when the scabbards used Ryou on him. For Kaido who doesn't know anything about Ryou, he refers Ryou to Oden's haki. That's why when Scabbard and Zoro used on him, he calls/sees that at Oden's haki. Also why he didn't understand how Luffy hurt him with Red Roc at first.
No there is no haki of Oden here.