From my experience, dog owners and people in general tend to see human-like patterns in dog behavior even when more simple explanations ("looking at the world through dog's eyes") have better predictive power.
As many dog owners would tell, dogs learn how to show their needs (staring at a door to be let outside, bringing a leash when they want to go for a walk, or a toy when they want to play, etc.). I find it pretty impressive that Bunny learned to communicate her needs through the board, but from what I've seen, I don't really think there's much evidence for some of the complex behaviour this post and the owner suggested there is.
I think that she learned which words or parts of the board to use in specific contexts (questions about time and place, mirror) but I don't it shows she can tell time or recognize herself in the mirror (AFAIK, no dog can do that). On the other hand, I think that she can somewhat describe the world around her and I'm really curious what is the extent of this ability.
A lot of the behavior from the videos (eg. the negotiations) reminds me of a dog training technique when you let the dog try things and reward them when they do the thing you want. Dogs can get pretty creative this way and can generate novel behavior (which can be "shaped" into a more complex one). This way, Bunny learns sequences of words that generate amusement or other positive feedback (eg. the poop conversation).
Also, Bunny and her owner have a very strong bond and there are definitely many nonverbal cues happening.
That being said, I updated my model of dog cognitive skills and how can it be tested. I'm most excited about testing the ability to generalize and I expect I'll look into it further.