He clearly didn't, he caught him off guard, based on how they exchanged kicks it's kind of obvious that it's more like king's physical strength>= sanji's, or the other way around depending on how he fought king and queen before being thrown away
1. sanji is the person who caught king offguard. there's no way king caught sanji offguard lol. sanji very clearly knew king was coming after him.
2. king was aiming that kick at momonosuke and to kill momo, not sanji. he was not even aware that sanji was there. as mihawk said, only a fool would go all out to kill a rabbit. king's second kick was aimed at sanji and sanji had to use the raid suit + armament to block it.
3. king already had sanji by the throat well before sanji threw momo away.
4. the beak attack did significant damage. sanji was bleeding the very next panel we see him. stop acting like sanji himself didnt say that he would die. and no, that isnt sarcasm. luffy would never react that way to the beak attack if sanji was being sarcastic.