It starts with "You're okay with this? Not just another target, you know." At that point in the story, we know Osiris is going after Chief, we know what Buck thinks of Chief (same as 99% of the UNSC), and we're about to learn what Locke thinks of Chief. That makes sense to me. Buck is using a pronoun instead of a noun to describe the mission, because the mission is what's on everyone's mind, audience and characters alike. He doesn't need to be specific, and Buck doesn't seem like the type of guy who gets all prim and proper about grammar and conversational etiquette. He sounds like a soldier.

It ends with "You're not the only one here because of him", and Locke walks away. Locke is a silent and stoic type who doesn't want to talk about his feelings, so he doesn't. We know he has some kind of history with Chief, and we know he doesn't want to talk about his past.

I dunno mate, it seems like both of these lines are just serving to help establish the characters and how they act. Buck is casual, Locke has a stick up his ass. Buck respects the Chief, Locke does too but he's got a job to do. They're not how a perfectly normal person would start or end this conversation, but we're not being shown perfectly normal people. We're being shown a guy with an above average amount of social intelligence, and a guy with none. These lines make sense and they give us information. They tell us that the mission to hunt down the Chief is on everyone's mind. They tell us who these characters are and what they value.