Granted that I didn't play all that far, but I found the dialogue to be the opposite of gritty. 90% of the dialogue I read in ~6 hours was goofy. Usually intentionally so.
That's my feeling too, I'm fine with it but I wish they didn't make it so constant in most of the dialogues.
For example, after each answer from an NPC you need to say whether you'd like to leave or to ask something else - which isn't necessary, they could just display the remaining questions. Those two options are often said with some bad/goofy humour. Part of the style, but a little heavy IMO.
Maybe @vanedor; meant the general situation was described as gritty, being post-apocalyptic, everyone trying to survive as they can, etc?