Apparently, Karino has been paying attention to this pair enough to see that Yatori manipulates Yakuri by both fanning Yakuri's poor self-esteem and catering to Yakuri's attempts to cover for the weakness with bravado and bullying. So Karino would have fought for the card, but recognized that Yatori wanted to fail to get it, which is why it is cunning for Yatori to pretend to be afraid and give the card up. If Yatroi got the card and didn't give it to Yakuri, then Yakuri would no longer believe only Yatori likes him and it may break Yakuri's fragile hold on who he thinks he is (which would spoil what Yatori likes about the relationship). If Yatori gives Yakuri the card, then everyone will flatter Yakuri and Yaluri will be able to be with oter people sexually. Yatori knows the best play for him is to keep things exactly as they are, so that Yakuri is always too insecure to grow out of his conceits and bullying, and Yakuri is therefore always emotionally dependent on Yatori and will always let Yatori do as he pleases.
TLDR: Yatori is playing dumb and obedient, but he is actually manipulating Yakuri.
Karino saw through it all since he used to do exactly the same thing when Azuza was king. But, since Azuza's more proud than Yukari, he needed the king card...
Can someone explain why he says "what a cunning guy" at the end? I don't get it