This topic is quite closely related to the argument about dialogue in visual mediums (namely video games, movies and tv) in general; namely that you always have to show and not tell. It's true that the strongest way to bring across the impact and importance of events in a story is to show them happening. However, if this was a requirement, then just about every tv show, movie and game with a plot would be riddled with flashbacks as anytime one character tried to relate to another something that had occurred, the audience had to be shown the event as it happened.
Dialogue may seem very dry and dull, but only if a) it's done poorly, with little emotion behind it and no apparent interest from the characters or b) the audience/players don't give a damn about the story. There's no doubt that A occurs in games with dialogue in them; I'm wondering, though, how often B's the case. When we look back at older movies, the ones that are by-and-large considered superior to modern ones, a lot of them are dialogue heavy. I don't find it hard to imagine a lot of the gaming community trying to watch films like "Casablanca", "12 Angry Men", the original "Ransom" and "The Sting" and having trouble because they have to pay close attention to the dialogue to understand what's going on, what the characters are going through and what they've been through. I wonder if maybe it's a mark of society and how much we've allowed instant gratification to seep into our mentality that we're not interested in entertainment that requires us to pay attention and think as opposed to just sitting by and getting information blasted at us. It's not enough that a character whose a shell-shocked soldier tells us he's one of the few survivors of a battle where 2,000 troops went in and only 50 came back alive, that the bombs fell so hard it felt like the earth was getting torn in half...no, we've got to SEE it happening because our puddle-shallow imaginations can't conjure up the mental images required for us to realize "it was really fucking scary."
In conclusion, yes, dialogue needs to sound natural and convey some emotion in order to be engaging. But at the same time, players might also want to try and appreciate subtlety and give the words coming out of character's mouths some attention. You know, as opposed to hitting the skip button as fast as possible because something isn't exploding or getting decapitated on screen.