He already stated that the one to defeat him will be joyboy , he only got captured to eat , he searched for a place to die , tho i dont think dying to marines is something he would've liked
Who cares how he was captured it doesn't have anything to do with the fact he survived 40 death sentences and over 1,000 torture matters while receiving a single scar.
Kaido doesn't want to die anywhere he wants to be killed in battle because he believes that is what completes a person. That's why he was disappointed when they Scabbards couldn't kill him.
Luffy beat him but unfortunately just another person who failed to kill him. If Kaido is killed by the magma than the magma killed him not Luffy. There's no reason for Kaido to stop fighting and give up on life just because he met another person who could defeat him but not kill him. It is already happened seven other times. He will consider Joyboy just another opponent that can't kill him.
Kaido dangerous people value and work in battle. If Joyboy can't kill him then information he thought about Joyboy based on what he either heard or read doesn't meet his expectations.