I dunno where David said it but he made it pretty clear that it was only playable by dev standards. Granted I have no idea how much work it still needs from that stage but yeah. It certainly isn't playable by any gamer's standards.
Anyway if it is delayed again whoever is wearing the Boss Hat seriously needs to rain in the team's ambition so that it matches their ability.
You need to take into account how Bioware makes games. If I understand this correctly, it's not a linear process following the storyline, but a process of refinement that proceeds from the "bullet points" of the game, so to speak, to the lines in-between. Compared to a book, that would mean you first write the titles of all chapters and outline what's going into them in a very general sense, and then gradually add content the readers will see in the finished product.
That's why a game can be technically playable at an early stage of development. You can play it, yes, but you'll see wireframes and placeholder graphics instead of real artwork, placeholder signs for scenes saying "dialogue between X and Y about Z" without any actual dialogue being present. At a later stage, you may see the subtitles but the spoken lines aren't in yet, and you have the real models but textures are missing. And so on.
Because of that, a rushed game doesn't necessarily appear unfinished in terms of story. It appears unpolished instead. If it appears unfinished or inconsistent in terms of story, that's more likely to be the result of cuts. For a rushed game, see DA2. For a game riddled by cut content, see ME3. At least that's what I suspect.