I guess Sanji looks like this permanently after not getting a fight at WCI
His nose is bent, now it's really close to his mouth.
Drawings in most manga are not consistent. King is only drawn once in his beast form before his clash with Sanji, and it just happens to be a straight beak. After he has a straight and curved beak multiple times just like Oda drew Morgans at WCI. It looks exactly the same, it's a stylized choice that depends on the scene, the angle, how he's drawing it and more.
King made zero remarks to being injured by Sanji, nor his beak. He even goes back to human form and looks completely normal, with no indication that he and Sanji even clashed.
This is unlike the instance where Blueno made a contorted in pain once Sanji nearly broke through his tekkai.