As far as Antonius' hand goes, it's somewhat unlikely that he's got the Ad in his hand because it was a limped pot, which greatly widens Patrick's preflop calling range; he could have virtually any flush draw. When Patrick calls his flop bet, Ivey knows that since he only has a 7 kicker, if Patrick has Kx, Patrick's K is almost certainly larger (if he has a K at all). Also, and most importantly, it's not a certainty that Patrick has a hand at all, since he is the BTN, and will theoretically be floating this flop a fair amount of the time, since it's a very dry, paired board, and Patrick knows that Ivey is perfectly capable of stealing in this spot. In sum, Patrick's hand is pretty face-up as either Kx where x > 7, a flush draw which could be Ax diamonds but is probably lower, or total air. He could obv have 22 or medium PP that he decided to peel with, but those are far less likely.
Benyamine c/c flop, which is going to be a flush draw the vast majority of the time on that board, and very occasionally some odd played pairs 77-99, and 22 for a slowplayed FH, but again flushdraws makes up most of his range.
Ott Benyamine checks again, Ivey knows that if he had the best hand otf, he no longer does because someone's obv got a flush or a better K, he checks, Antonius bets 10k into a 14k pot. That's a pretty large bet, which largely confirms to Ivey that Patrick's got a decent Kx hand that doesn't want to see another diamond otr. Benyamine calls fairly quickly, so it's pretty obv he's got a small flush. Benyamine would c/r the nut flush probably about 1/2 the time here at least, so his c/c is indicative of a small flush. Ivey presumably calls to, I dunno, bink either a 7 otr, or more probably to bluff a river diamond.
River is a diamond, Benyamine checks a 3rd time, which effective turns his hand face up as a small flush. From Patrick's bet sizing ott, he knows that Patrick probably didn't want to see another diamond, meaning he's obv not got the Ad. Knowing that neither player has Ad, he pots river knowing that he could easily show up with Ad himself. He could've bet flop with a backdoor flush draw in a steal attempt, c/c turn to control pot and draw out on lower flushes that may pay him otr, and leads river knowing that Antonius will always check down his larger Kx hand.