@Van_ I don't disagree, I think there is a lot of emphasis on the situation that makes it seem overdramatic. But it's important to remember a lot of this is character interaction based. Hachiman is in turmoil and dealing with a lot of decisions and doubt. Slap on the fact yukinoshita wants to grow independent and yui's feelings she sacrificed to let hachiman do his thing. The dynamic we had earlier in the series that allowed for comedy is gone. Instead they are going their own way to attack a problem that doesn't affect them as a group/club but as individuals. And while it does seem 'overdramatic' it's certainly is a lot better than most romance series that throw characters against a bus or down the stairs to keep plot moving.
I will admit though, I feel that yui's reaction is slightly unwarranted. It isn't like he chose yukino over her or anything. This wasn't that kind of moment.
But tbf, this does mean he expressed desire to want to be there for yukino and yui can take that as him expressing feelings for yukino. It's a reaction from her that was built up over quite a few chapters of her seeing how yukino feels about him (like finding the picture). If we had more of yui's monologue overtime instead of just this small bit then we'd understand better.