The time has finally come for the exchange. Not very many words exchanged, as all three are tense. From the little we can see of Akihito's face he apparently recognizes Kirishima, even if just a little. Kirishima knows his priorities--get Akihito first, then the deed. Can't help but wonder if Akihito is worried that there's only one guy, and not even the big guy (Suoh)
Kirishima could perhaps overlook the initial clinging as being unused to the boat or general nervousness, but even he knows Akihito well enough that the grip and shaking are not characteristic of Akihito at all. Whether his concern is for Akihito himself or for what it means in regards to his job is difficult to say, but given how close he is to Asami (appears to be 2nd in command) it's pretty safe to say that he prioritizes Akihito highly; judging from the overall behavior of Asami men, he probably actually cares about Akihito a bit--they've spent time together (probably not on purpose, but it counts) and he doesn't shake off Akihito as if he were an annoyance. For Akihito, now that Yuri has the deed, there is enough relief of tension that he can ask for the only thing he wants, his desperation showing through.
Kirishima doesn't even wait for Yuri to go away before he calls to reassure that Akihito is with him and safe--because apparently Asami's first words were to question if Akihito was alright (like he probably easily could have told Kirishima to shoot Yuri and taken the deed, too, since Mikhail didn't think to send more than one guy or have Yuri contact him afterwards). No, Kirishima, he's not really fine, but we'll forgive you cause you don't know him that well plus you're still ready to take a bullet for him when that Russian homophobic mobster with an irrational amount of misplaced anger decides to start shooting.